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Proceedings of the American Mathematical Society

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

 

 

Intersections of $ \Gamma $-isotype subgroups in abelian groups


Author: Jindřich Bečvář
Journal: Proc. Amer. Math. Soc. 86 (1982), 199-204
MSC: Primary 20K21
DOI: https://doi.org/10.1090/S0002-9939-1982-0667272-9
MathSciNet review: 667272
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Abstract: A subgroup $ H$ of an abelian group $ G$ is an intersection of isotype subgroups of $ G$ if and only if, for each prime $ p$, if $ x + H$ is a coset of order $ p$ then there is another coset of order $ p$ containing an element $ y$ of order $ p$ such that $ h_p^* (x) \leqslant h_p^*(y)$. A subgroup $ H$ of $ G$ is isotype in $ G$ if and only if, for each prime $ p$, every coset $ x + H$ of order $ p$ contains an element y of order $ p$ such that $ h_p^*(x)h_p^*(y)$


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DOI: https://doi.org/10.1090/S0002-9939-1982-0667272-9
Keywords: Abelian groups, isotype, $ \Gamma $-isotype subgroups
Article copyright: © Copyright 1982 American Mathematical Society