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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The number of permutational products of two finite groups


Author: Norman R. Reilly
Journal: Proc. Amer. Math. Soc. 25 (1970), 507-509
MSC: Primary 20.52
DOI: https://doi.org/10.1090/S0002-9939-1970-0258968-3
MathSciNet review: 0258968
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Abstract: Let $H$ be a subgroup of the two finite groups $A$ and $B$. Let $\mathcal {S}\;(\mathcal {J})$ be the set of transversals of the left cosets of $H$ in $A\;(B)$, and consider $A\;(B)$ as a permutation group on $\mathcal {S}\;(\mathcal {J})$ where the action is by left multiplication. If ${n_A}\;({n_B})$ is the number of orbits under the action of $A\;(B)$ then the number of nonisomorphic permutational products of $A$ and $B$ amalgamating $H$ is bounded by ${n_A}{n_B}$.


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Keywords: Permutational products of groups
Article copyright: © Copyright 1970 American Mathematical Society