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Subgroups of Conjugate Classes in Extensions

Published online by Cambridge University Press:  20 November 2018

John E. Burroughs  and
James A. Schafer
John E. Burroughs
Affiliation:
University of Michigan, Ann Arbor, Michigan
James A. Schafer
Affiliation:
University of Michigan, Ann Arbor, Michigan
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Often in various mathematical problems one encounters an extension B of the group G by the group π in which one wishes to extract certain information about B from information given in terms of G, π, the action of π on G, and the class of the extension in H2(π, centre G). An example of this type of problem is to determine some intrinsically defined subgroup of B, for instance the centre of B, given knowledge of the corresponding subgroup for G and π, and, of course, the usual information concerning the extension.

In this paper we shall use the fact that any extension is congruent to a crossed product extension [2] to investigate a class of subgroups which naturally generalizes the notion of the centre. The definition of this class appears in § 3.

1. Let

by an extension of G by π.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 4 , 01 August 1970 , pp. 773 - 783
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Baer, R., Finiteness properties of groups, Duke Math. J. 15 (1948), 1021–1032.Google Scholar
2. MacLane, S., Homology (Springer, Berlin, 1963).Google Scholar
3. Newmann, B. H., Groups with finite classes of conjugate elements, Proc. London Math. Soc. 1 (1951), 178–187.Google Scholar