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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On direct products of regular $ p$-groups


Author: J. R. J. Groves
Journal: Proc. Amer. Math. Soc. 37 (1973), 377-379
MSC: Primary 20D15
MathSciNet review: 0323891
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Abstract: We prove that, for each prime p, there exists a regular p-group $ H(p)$ with the property that, if G is a regular p-group and $ G \times H(p)$ is regular, then the derived group of G has exponent p. This provides a strong converse to a theorem of Grün.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0323891-5
PII: S 0002-9939(1973)0323891-5
Keywords: Finite p-group, regular, direct product, p-abelian
Article copyright: © Copyright 1973 American Mathematical Society