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Algorithms for Groups
, 1994
"... Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational group theory may be used to gain insight into the general str ..."
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Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational group theory may be used to gain insight into the general structure of algebraic algorithms. This paper examines the basic ideas behind some of the more important algorithms for finitely presented groups and permutation groups, and surveys recent developments in these fields.
An Invitation to Computational Group Theory
 Groups' 93  Galway/St. Andrews, volume 212 of London Math. Soc. Lecture Note Ser
, 1995
"... Algebra" in 1967 [Lee70]. Its proceedings contain a survey of what had been tried until then [Neu70] but also some papers that lead into the Decade of discoveries (19671977). At the Oxford conference some of those computational methods were presented for the first time that are now, in some ..."
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Algebra" in 1967 [Lee70]. Its proceedings contain a survey of what had been tried until then [Neu70] but also some papers that lead into the Decade of discoveries (19671977). At the Oxford conference some of those computational methods were presented for the first time that are now, in some cases varied and improved, work horses of CGT systems: Sims' methods for handling big permutation groups [Sim70], the KnuthBendix method for attempting to construct a rewrite system from a presentation [KB70], variations of the ToddCoxeter method for the determination of presentations of subgroups [Men70]. Others, like J. D. Dixon's method for the determination of the character table [Dix67], the pNilpotentQuotient method of I. D. Macdonald [Mac74] and the ReidemeisterSchreier method of G. Havas [Hav74] for subgroup presentations were published within a few years from that conference. However at least equally important for making group theorists aware of CGT were a number of applications of...
The 2Modular Decomposition Matrices of the Symmetric Groups S15, S16, and S17
 S15, S16, and S17, Comm. Algebra 28
"... In this paper the 2modular decomposition matrices of the symmetric groups S_15, S_16, and S_17 are determined by application of methods from computational representation theory, in particular condensation techniques, and by using the computer algebra systems GAP, MOC, and the MeatAxe. ..."
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In this paper the 2modular decomposition matrices of the symmetric groups S_15, S_16, and S_17 are determined by application of methods from computational representation theory, in particular condensation techniques, and by using the computer algebra systems GAP, MOC, and the MeatAxe.
The 7Modular Decomposition Matrices Of The Sporadic O'Nan Group
 J. London Math. Soc
, 1999
"... The determination of the modular character tables of the sporadic O'Nan group, its automorphism group and its covering group is completed by the calculation of the 7modular decomposition numbers. The results are obtained with the assistance of the systems GAP, MOC, and MeatAxe, and by appl ..."
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The determination of the modular character tables of the sporadic O'Nan group, its automorphism group and its covering group is completed by the calculation of the 7modular decomposition numbers. The results are obtained with the assistance of the systems GAP, MOC, and MeatAxe, and by applying new condensation methods.
ON THE TRACE MAP BETWEEN ABSOLUTELY ABELIAN NUMBER FIELDS OF EQUAL CONDUCTOR
, 2006
"... Let L/K be an extension of absolutely abelian number fields of equal conductor, n. If TL/K: L → K denotes the trace map, then TL/K(OL) is an ideal in OK. Let I(L/K) denote the norm of TL/K(OL) over Q, i.e. [OK: TL/K(OL)]. Sharpening the main result of Girstmair in [6], we determine I(L/K) exactly fo ..."
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Let L/K be an extension of absolutely abelian number fields of equal conductor, n. If TL/K: L → K denotes the trace map, then TL/K(OL) is an ideal in OK. Let I(L/K) denote the norm of TL/K(OL) over Q, i.e. [OK: TL/K(OL)]. Sharpening the main result of Girstmair in [6], we determine I(L/K) exactly for any such L/K: if e = v2(n) and m = n/2e, then
Article Submitted to Journal of Symbolic Computation Constructing Transitive Permutation Groups
"... This paper presents a new algorithm to classify all transitive subgroups of the symmetric group up to conjugacy. It has been used to determine the transitive groups of degree up to 30. 1. ..."
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This paper presents a new algorithm to classify all transitive subgroups of the symmetric group up to conjugacy. It has been used to determine the transitive groups of degree up to 30. 1.