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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

1. Dornhoff, L., Group representation theory, Dekker, New York, 1967.Google Scholar
2. Huppert, B., Endliche Gruppen I, Springer Verlag, Berlin, 1967.Google Scholar
3. Scott, W. R., Group Theory, Prentice Hall, Englewood Cliffs, New Jersey, 1964.Google Scholar