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

A property of finite $ p$-groups


Author: Shoichi Kondo
Journal: Proc. Amer. Math. Soc. 67 (1977), 35-37
MSC: Primary 20C15
MathSciNet review: 0460439
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Abstract: Let $ R(G)$ denote the character ring of a finite group G and let $ \Lambda $ be a commutative ring with identity. In this paper we show that if $ G \ne \{ 1\} $, then $ \Lambda { \otimes _Z}R(G)$ has only one maximal ideal if and only if G is a p-group and $ \Lambda $ has only one maximal ideal m such that $ \Lambda /\mathfrak{m}$ is of characteristic p.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0460439-2
PII: S 0002-9939(1977)0460439-2
Keywords: Finite p-group, character ring, Steinitz ring
Article copyright: © Copyright 1977 American Mathematical Society