Publications - Bettina Eick


This web page lists my publications, theses and other manuscripts.


Recently accepted
  • Enumeration of groups of order p^n q for n at most 5. With T. Moede. J. Algebra.
  • Enumeration of nilpotent associative algebras of class 2 over arbitrary finite fields. With M. Wesche. J. Algebra.
  • Polynomials describing the multiplication in finitely generated torsion-free nilpotent groups. With A. Cant. J. Symb. Comput.
  • Constructing groups of 'small' order: Recent results and open problems. With M. Horn and A. Hulpke. DFG Proceedings.
  • Classifying nilpotent associative algebras: small coclass and finite fields. With T. Moede. DFG Proceedings
arXiv reports
  • Enumeration of groups whose order factorises in at most 4 primes. ArXiv 1702.02616
  • Deciding if a variety forms an algebraic group. With J. Abbott. ArXiv 1511.07627.
  • Graded Lie algebras of Cartan type in characteristic 2. With T. Brough. ArXiv 1510.02289.
  • Infinite sequences of p-groups with fixed coclass. With D. Feichtenschlager. ArXiv 1006.0961
  • Polycyclic groups: A new platform for cryptology? With D. Kahrobaei. ArXiv math/0411077
Papers
  • Coclass theory for finite nilpotent associative algebras: Algorithms and a periodicity conjecture. With T. Moede. Exp. Math. 26, 267 -- 274 (2017)
  • The torsion free nilpotent groups of Hirsch length at most 5. With A.-K. Engel. Groups Complex. Cryptol. 9, 55 -- 75 (2017)
  • Cochain sequences and the Quillen category of a coclass family. With D. Green. J. Australian Math. Soc. 102, 185 -- 204 (2017)
  • On p-groups of maximal class with 'large' automorphism group. With H. Dietrich. J. Group Theory 20, 227 -- 256 (2017).
  • The automorphism group of a finitely generated virtually abelian group. Groups Complex. Cryptol. 8, 35 -- 45 (2016)
  • The isomorphism problem for graded algebras and its application to mod-$p$ cohomology rings of small $p$-groups. With S. King. J. Algebra 452, 487 -- 501 (2016)
  • Nilpotent associative algebras and coclass theory. With T. Moede. J. Algebra 434, 249 -- 260 (2015)
  • Group extensions with special properties. With A. Distler. Groups Complex. Cryptol. 7, 1 -- 10 (2015).
  • The Quillen categories of $p$-groups and coclass theory. With D. Green. Israel J. Math. 206, 183 -- 212 (2015).
  • Metabelian p-groups and coclass theory J. Algebra 421, 102 -- 118 (2014).
  • Approximating generators for integral arithmetic groups. Mathematical Software - ICMS 2014, 83 -- 86, Lecture notes in Comput. Sci. 8592, Springer (2014).
  • The constructive membership problem for discrete free subgroups of rank 2 of SL(2,R). With M. Kirschmer and C.R. Leedham-Green. LMS J. Comput. Math. 17, 345 -- 359 (2014), 166--182.
  • The construction of finite solvable groups revised. With M. Horn. J. Algebra 408, 166 -- 182 (2014).
  • On the classification of groups of prime-power order by coclass: The 3-groups of coclass 2. With C.R. Leedham-Green, M.F. Newman and E.A. O'Brien. J. Algebra Comput. 23, 1243 -- 1288 (2013).
  • On efficient presentations for infinite families of 2-groups with fixed coclass. With H. Abdolzadeh. Algebra Colloquium 20, 561 -- 572 (2013).
  • Coclass theory for nilpotent semigroups via their associated algebras. With Andreas Distler. J. Algebra 373, 491 -- 501 (2013).
  • Computing Hall subgroups of finite groups. With A. Hulpke. LMS J. Comput. Math. 15, 205 -- 218 (2012).
  • Collection by polynomials in finite p-groups. Contemp. Math. 582, 95 -- 103 (2012).
  • Addendum to "On the groups of cube-free order", J. Algebra 292, 122-137 (2005). Contemp. Math. 582, 95 -- 103 (2012).
  • Schur multipliers and the Lazard correspondence. With Max Horn and Seiran Zandi. Arch. Math. 99, 217 -- 226 (2012).
  • Computing nilpotent quotients of associative algebras and algebras satisfying a polynomial identity. IJAC 21 (8), 1339--1355 (2011).
  • Computing with matrix groups over infinite fields. With A. Detinko and D. Flannery. In Proceedings of Groups St. Andrews 2009, 256--270 (2011).
  • The modular isomorphism problem for the groups of order 512. With A. Konovalov. In Proceedings of Groups St. Andrews 2009, 375--383 (2011).
  • Computation of low-dimensional (co)homology groups for infinite sequences of p-groups with fixed coclass. With D. Feichtenschlager. IJAC 21(4), 635--649 (2011)
  • Some new simple Lie algebras in characteristic 2. J.Symbol. Comput. 45, 943 -- 951 (2010)
  • Computing polycyclic quotients of finitely (L-)presented groups via Groebner bases. With M. Horn. In Proceedings of ICMS Conference 2010 (Kobe), 50--53 (2010).
  • Periodicities and p-groups of given rank, width and obliquity. With T. Rossmann. In Proceedings of the AMS Special Session 'Computational Group Theory' II, 11--24 (2010)
  • Computing faithful representations for nilpotent Lie algebras. With D. Burde and W. de Graaf. J. Algebra 322, 602 -- 612 (2009)
  • Constructing CF groups by coclass. With D. Feichtenschlager. Experimental Mathematics 18, 205 -- 211 (2009)
  • Computing $p$-groups with trivial Schur multiplicator. J. Algebra 322, 741 -- 751 (2009)
  • A nilpotent quotient algorithm for certain infinitely presented groups. With L. Bartholdi and R. Hartung. International J. Algebra Comput. 18, 1321 -- 1344 (2008)
  • Investigating p-groups by coclass with GAP. With H. Dietrich and D. Feichtenschlager. In Proceedings `AMS Special Session on Computational Group Theory' by Kappe, Magidin and Morse, AMS Contemp. Math. 470, 45 -- 61 (2008)
  • Computing automorphism groups and testing isomorphisms for modular group algebras. J. Algebra 320, 3895--3910 (2008)
  • On the classification of prime-power groups by coclass. With Charles Leedham-Green. Bull. Lond. Math. Soc. 40, 274 -- 288 (2008)
  • Computing the Schur multiplicator and the nonabelian tensor square of a polycyclic group. With W. Nickel. J. Algebra 320, 927 -- 944 (2008)
  • Schur multiplicators of finite p-groups with fixed coclass. Israel J. Math. 166, 157 -- 166 (2008)
  • Schur multiplicators of infinite pro-p-groups with finite coclass. Israel J. Math. 166, 147 -- 156 (2008)
  • Testing polycyclicity of finitely generated rational matrix groups. With B. Assmann. Math. Comp. 76, 1669 -- 1682 (2007)
  • On p-groups forming Brauer pairs. With Jürgen Müller. J. Algebra 304, 286 -- 303 (2006)
  • The class-breadth conjecture revisited. With M.F. Newman and E.A. O'Brien. J. Algebra (Comput. Sec.) 300, 384 -- 393 (2006)
  • Automorphism groups of 2-groups. J. Algebra (Comput. Sec.) 300, 91 -- 101 (2006)
  • On the maximal 2-extensions of Q with given ramification With Helmut Koch. Proc. St. Petersburg Math. Soc. (Russian)
  • Algorithms for crystallographic groups. With Bernd Souvignier. International Journal of Quantum Chemistry 106, 316 - 343 (2006)
  • On the number of infinite branches in the graph of all p-groups of coclass r. J. Group Theory 8, 687 - 700 (2005)
  • Computing polycyclic presentations for polycyclic rational matrix groups. With Björn Assmann. J. Symb. Comput. 40, 1269 -- 1284 (2005)
  • Computational Group Theory. Jahresberichte der DMV 107, Heft 3, 155 - 170 (2005)
  • On the groups of cube-free order With Heiko Dietrich. J. Algebra 292, 122 - 137 (2005)
  • On the determination of the uniserial space groups with a given coclass. J. London Math. Soc. (2) 71, 622 - 642 (2005)
  • Special polycyclic generating sequences for finite soluble groups. With John J. Cannon and Charles R. Leedham-Green. J. Symb. Comput. 38, 1445 - 1460 (2004)
  • Computing the automorphism group of a solvable Lie algebra. Lin. Alg. Appl. 382, 195 - 209 (2004)
  • Computations with almost-crystallographic groups. With Karel Dekimpe. Proceedings "Groups St. Andrews in Oxford", 2001, C.M. Campbell, E.F. Robertson, G.C. Smith, eds., London Math. Soc. 110 - 119 (2003)
  • When is the automorphism group of a virtually polycyclic group virtually polycyclic? Glasgow. J. Math. 45, 527 - 533 (2003)
  • On the orbit-stabilizer problem for integral matrix actions of polycyclic groups. With Gretchen Ostheimer. Math. Comp. 72, (Number 243) 1511 - 1529 (2003)
  • The solvable primitive permutation groups of degree at most 6560. With Burkhard Höfling. Electronic J. LMS 6, 29--39 (2003)
  • Orbit-stabilizer problems and computing normalizers for polycyclic groups. J. Symb. Comput. 24, 1 - 19 (2002)
  • Constructing automorphism groups of $p$-groups. With C. R. Leedham-Green and E. A. O'Brien. Comm. Alg. 30(5), 2271 - 2295 (2002)
  • Computational aspects of group extensions and their applications in topology. With Karel Dekimpe. Exp. math. 11, 183 - 199 (2002)
  • A millennium project: constructing small groups. With Hans Ulrich Besche and E. A. O'Brien. International Journal of Algebra and Computation 12, 623 - 644 (2002)
  • Computing subgroups by exhibition in finite solvable groups. With Charles R. B. Wright. J. Symb. Comput. 33(2), 129 - 143 (2002)
  • The groups of order at most 2000. With Hans Ulrich Besche and E. A. O'Brien. Electronic Research Announcemen Amer. Math. Soc. 7, 1-4 (2001)
  • On the Fitting subgroup of a polycyclic-by-finite group and its applications. J. Algebra. 242, 176 - 187 (2001)
  • The groups of order q^n * p. With Hans Ulrich Besche. Comm. Alg. 29(4), 1759 - 1772 (2001)
  • Computing with infinite polycyclic groups. Proceedings "Groups and Computation III" 1999, W. M. Kantor and A. Seress, ed., de Gruyter, 139 - 153 (2001)
  • Computing the maximal subgroups of a permutation group I. With Alexander Hulpke. Proceedings "Groups and Computation III" 1999, W. M. Kantor and A. Seress, ed., de Gruyter, 155 - 168 (2001)
  • On groups of automorphisms of residually finite groups. With Ulderico Dardano and Martin Menth. J. Algebra. 231, 561 - 573 (2000)
  • Enumerating p-groups. With E. A. O'Brien. J. Austral. Math. Soc. (Series A) 67, 191 - 205 (1999)
  • Construction of finite groups. With Hans Ulrich Besche. J. Symb. Comput. 27 (4), 387 - 404 (1999)
  • The groups of order at most 1000 except 512 and 768. With Hans Ulrich Besche. J. Symb. Comput. 27 (4), 405 - 413 (1999)
  • The groups of order 512. With E. A. O'Brien. Proceedings "Abschlusstagung des DFG Schwerpunktes Algorithmische Algebra und Zahlentheorie" 1997, B.H. Matzat, G.-M. Greuel and G. Hiss, eds, Springer 379 - 380 (1998)
  • Computing maximal subgroups and Wyckoff positions of space groups. With Franz Gähler and Werner Nickel. Acta Kryst A 53, 467 - 474 (1997)
  • Special presentations for finite soluble groups and computing (Pre-) Frattini subgroups. Proceedings "Groups and Computation II" 1995, L. Finkelstein and W. M. Kantor, ed., Amer. Math. Soc. 101 - 112 (1997)
  • The converse of a theorem of W. Gaschütz on Frattini subgroups. Math. Z. 224, 103 - 111 (1997)
  • The converse of a theorem of Gaschütz (Announcement). Proc. 12th Annual Victorian Algebra Conference, 39 (1994)
Books
  • Handbook of Computational Group Theory. Derek Holt, Bettina Eick and Eamonn O'Brien. CRC Press, ISBN 1-58488-372-3 (2005)
  • 4000 Jahre Algebra. H.-W. Alten, A. Djafari Naini; B. Eick; M. Folkerts; H. Schlosser; K.-H. Schlote; H. Wesemüller-Kock; H. Wussing. Springer Spektrum, ISBN 978-3-642-38238-3/hbk; 978-3-642-38239-0/ebook (2014).
  • Charakterisierung und Konstruktion von Frattinigruppen mit Anwendungen in der Konstruktion endlicher Gruppen. Bettina Eick. Aachener Beiträge zur Mathematik, Band 17, ISBN 3-86073-426-1 (1996)
Theses
  • Diplomarbeit (RWTH Aachen, 1993): Spezielle PAG Systeme im Computeralgebrasystem GAP.
  • Doktorarbeit (RWTH Aachen, 1996): Charakterisierung und Konstruktion von Frattinigruppen mit Anwendungen in der Konstruktion endlicher Gruppen.
  • Habilitationsschrift (Kassel, 2001): Algorithms for polycyclic groups.
Reports
  • Linear equations over finite abelian groups. Report.
  • Quotient algorithms generalize to finitely L-presented groups. Report.

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