Computing with finite groups
نویسنده
چکیده
• This work is protected by copyright and other intellectual property rights, which are retained by the thesis author, unless otherwise stated. • A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. • This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the author. • The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the author. • When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given. Summary The character table of a finite group G is constructed by computing the eigenvectors of matrix equations determined by the centre of the group algebra. The numerical character values are expressed in algebraic form. A variant using a certain sub-algebra of the centre of the group algebra is used to ease problems associated with determining the conjugacy classes of elements of G. The simple group of order 50,232,960 and its subgroups PSL(2,1'7) and PSL(2,19) are constructed using general techniques.
منابع مشابه
COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS
Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...
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