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Numbers Of Conjugacy Class Sizes And Derived Lengths for A-Groups

Published online by Cambridge University Press:  20 November 2018

Mary K. Marshall
Mary K. Marshall*
Affiliation:
Department of Mathematics, Illinois College, Jacksonville, IL 62650, U.S.A.
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Abstract

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An A-group is a finite solvable group all of whose Sylow subgroups are abelian. In this paper, we are interested in bounding the derived length of an A-group G as a function of the number of distinct sizes of the conjugacy classes of G. Although we do not find a specific bound of this type, we do prove that such a bound exists. We also prove that if G is an A-group with a faithful and completely reducible G-module V, then the derived length of G is bounded by a function of the number of distinct orbit sizes under the action of G on V.

Keywords

20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 346 - 351
Copyright
Copyright © Canadian Mathematical Society 1996

References

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