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Finite Linear Groups of Degree Seven. I

Published online by Cambridge University Press:  20 November 2018

David B. Wales
David B. Wales*
Affiliation:
California Institute of Technology, Pasadena, California
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1. 1. This paper is the second in a series of papers discussing linear groups of prime degree, the first being (8). In this paper we discuss only linear groups of degree 7. Thus, G is a finite group with a faithful irreducible complex representation Xof degree 7 which is unimodular and primitive. The character of Xis x- The notation of (8) is used except here p= 7. Thus Pis a 7-Sylow group of G.In §§ 2 and 3 some general theorems about the 3-Sylow group and 5-Sylow group are given. In § 4 the statement of the results when Ghas a non-abelian 7-Sylow group is given. This corresponds to the case |P| =73 or |P|= 74. The proof is given in §§ 5 and 6. In a subsequent paper the results when Pis abelian will be given.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1042 - 1053
Copyright
Copyright © Canadian Mathematical Society 1969

References

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