Publications - Bettina Eick


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Preprints
  • The modular isomorphism problem for the groups of order 512. With A. Konovalov. Submitted. (Pdf)

  • Isomorphism testing for Lie algebras over finite fields and simple Lie algebras over the field with two elements. Submitted. (Pdf)

  • On efficient presentations for infinite families of 2-groups with fixed coclass. With H. Abdolzadeh. Submitted. (Pdf)

  • Computing with matrix groups over infinite fields. With A. Detinko and D. Flannery. Accepted for Proceedings of Groups St. Andrews 2009. (Pdf)

  • Investigating some self-similar groups via nilpotent quotients. With R. Hartung. Submitted. (Pdf)

  • A polycyclic quotient algorithm. With A.C. Niemeyer and O. Panaia. Submitted. (PS / Dvi)

  • Periodicities and p-groups of given rank, width and obliquity. With T. Rossmann. Accepted for the Proceedings of the AMS Special Session 'Computational Group Theory' (Pdf)


Papers
  • Computing faithful representations for nilpotent Lie algebras. With D. Burde and W. de Graaf. J. Algebra 322, 602 -- 612

  • 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), English Version: (Pdf)

  • Algorithms for crystallographic groups. With Bernd Souvignier. International Journal of Quantum Chemistry 106, 316 - 343 (2006) (PS / Dvi)

  • 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. Electron. Res. Announc. 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)

  • 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 (1993): Spezielle PAG Systeme im Computeralgebrasystem GAP. RWTH Aachen (PS / Dvi)

  • Doktorarbeit (1996): Charakterisierung und Konstruktion von Frattinigruppen mit Anwendungen in der Konstruktion endlicher Gruppen. RWTH Aachen

  • Habilitationsschrift (2001): Algorithms for polycyclic groups. Universität Kassel


Reports
  • Report (2004): Polycyclic groups: A new platform for cryptology? With Delaram Kahrobaei (PS / Dvi)

  • Report (1995): Frattini group generation. (PS / Dvi )



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