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20d40 (secondary)

Journal of the London Mathematical Society (1)

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DERIVED SUBGROUPS OF PRODUCTS OF AN ABELIAN AND A CYCLIC SUBGROUP
M. D. E. CONDER, I. M. ISAACS
Journal:

Journal of the London Mathematical Society / Volume 69 / Issue 2 / April 2004

Published online by Cambridge University Press:

29 March 2004, pp. 333-348

Print publication:

April 2004
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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.