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DERIVED SUBGROUPS OF PRODUCTS OF AN ABELIAN AND A CYCLIC SUBGROUP

Published online by Cambridge University Press:  29 March 2004

M. D. E. CONDER  and
I. M. ISAACS
M. D. E. CONDER
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealandconder@math.auckland.ac.nz
I. M. ISAACS
Affiliation:
Mathematics Department, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USAisaacs@math.wisc.edu
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Abstract

Let $G$ be a finite group and suppose that $G = AB$, where $A$ and $B$ are abelian subgroups. By a theorem of Ito, the derived subgroup $G'$ is known to be abelian. If either of the subgroups $A$ or $B$ is cyclic, then more can be said. The paper shows, for example, that $G'{/}(G' \cap A)$ is isomorphic to a subgroup of $B$ in this case.

Keywords

20E34 (primary)20D40 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 333 - 348
Copyright
The London Mathematical Society 2004

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