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DERIVED SUBGROUPS OF PRODUCTS OF AN ABELIAN AND A CYCLIC SUBGROUP
Published online by Cambridge University Press: 29 March 2004
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.
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- The London Mathematical Society 2004
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