On direct products of regular $p$-groups
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- by J. R. J. Groves PDF
- Proc. Amer. Math. Soc. 37 (1973), 377-379 Request permission
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.References
- Reinhold Baer, Factorization of $n$-soluble and $n$-nilpotent groups, Proc. Amer. Math. Soc. 4 (1953), 15–26. MR 53109, DOI 10.1090/S0002-9939-1953-0053109-X
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- Otto Grün, Über das direkte Produkt regulärer $p$-Gruppen, Arch. Math. 5 (1954), 241–243 (German). MR 61602, DOI 10.1007/BF01899344
- Paul M. Weichsel, Regular $p$-groups and varieties, Math. Z. 95 (1967), 223–231. MR 204525, DOI 10.1007/BF01111525
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 377-379
- MSC: Primary 20D15
- DOI: https://doi.org/10.1090/S0002-9939-1973-0323891-5
- MathSciNet review: 0323891