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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
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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DOI: https://doi.org/10.1090/S0002-9939-1970-0258968-3
Keywords: Permutational products of groups
Article copyright: © Copyright 1970 American Mathematical Society