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

Units in modular group rings


Authors: D. B. Coleman and D. S. Passman
Journal: Proc. Amer. Math. Soc. 25 (1970), 510-512
MSC: Primary 20.40
MathSciNet review: 0262360
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Abstract: Let $ G$ be a finite $ p$-group and let $ U(G)$ denote the group of normalized units in the modular group ring of $ G$. If $ G$ is nonabelian, then it is shown that the nonregular group $ {Z_p}\wr {Z_p}$ is involved in $ U(G)$. Here $ {Z_p}$ is the group with $ p$ elements and $ {Z_p}\wr {Z_p}$ is wreath product.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0262360-5
PII: S 0002-9939(1970)0262360-5
Keywords: $ p$-group, group ring, group of units
Article copyright: © Copyright 1970 American Mathematical Society