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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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