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Focal Series in Finite Groups

Published online by Cambridge University Press:  20 November 2018

D. G. Higman
D. G. Higman*
Affiliation:
McGill University
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If there is given a subgroup 5 of a (finite) group G, we may ask what information is to be obtained about the structure of G from a knowledge of the location of S in G. Thus, for example, famed theorems of Frobenius and Burnside give criteria for the existence of a normal subgroup N of G such that G = NS and 1 = N ⋂ S, and hence in particular for the non-simplicity of G. To aid in locating S in G, and to facilitate exploitation of the transfer, we single out a descending chain of normal subgroups of S. Namely, we introduce the focal series of S in G by means of the recursive formulae

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 477 - 497
Copyright
Copyright © Canadian Mathematical Society 1953

References

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