Computer Algebra
Bettina Eick
Algorithms to compute with groups, associative algebras and Lie algebras
has been one of my main research projects throughout many years. Central
topics are algorithms for finite or infinite polycyclic groups,
classifications of various types of groups and rings and algorithms
to compute with associative algebras and Lie algebras. Below are my
main publications in these areas.
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Book and Survey
- Handbook of Computational Group Theory.
Derek Holt with Bettina Eick and Eamonn O'Brien.
CRC Press, ISBN 1-58488-372-3 (2005)
- Computational Group Theory. (Survey)
Jahresberichte der DMV 107, Heft 3, 155 - 170 (2005)
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Algorithms in Group Theory
- The conjugacy problem in GL(n,Z). With T. Hofmann
and E.A. O'Brien. J. London Math. Soc. (to appear)
- Polynomials describing the multiplication in
finitely generated torsion-free nilpotent groups.
With A. Cant. J. Symb. Comput.
- The automorphism group of a finitely generated
virtually abelian group. Groups Complex. Cryptol. 8, 35 -- 45 (2016)
- 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.
- 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).
- Computing with matrix groups over infinite
fields. With A. Detinko and D. Flannery.
In Proceedings of Groups St. Andrews 2009, 256--270 (2011).
- 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 $p$-groups with trivial Schur
multiplicator. J. Algebra 322, 741 -- 751 (2009)
- Computing the Schur multiplicator and the
nonabelian tensor square of a polycyclic group.
With W. Nickel. J. Algebra 320, 927 -- 944 (2008)
- Testing polycyclicity of finitely generated
rational matrix groups. With B. Assmann. Math. Comp. 76,
1669 -- 1682 (2007)
- Computing polycyclic presentations for
polycyclic rational matrix groups. With Björn Assmann.
J. Symb. Comput. 40, 1269 -- 1284 (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)
- 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)
- 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)
- On the Fitting subgroup of a polycyclic-by-finite
group and its applications. J. Algebra. 242, 176 - 187 (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)
- 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)
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Algorithms for Associative Algebras
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Computing nilpotent quotients of associative algebras and
algebras satisfying a polynomial identity.
IJAC 21 (8), 1339--1355 (2011).
- Computing automorphism groups and testing
isomorphisms for modular group algebras. J. Algebra 320,
3895--3910 (2008)
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Algorithms for Lie Algebras
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Some new simple Lie algebras in characteristic 2.
J.Symbol. Comput. 45, 943 -- 951 (2010)
- Computing faithful representations for
nilpotent Lie algebras. With D. Burde and W. de Graaf.
J. Algebra 322, 602 -- 612 (2009)
- Computing the automorphism group of a solvable
Lie algebra.
Lin. Alg. Appl. 382, 195 - 209 (2004)
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