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Minimal relative relation modules of finite $ p$-groups


Author: Mohammad Yamin
Journal: Proc. Amer. Math. Soc. 118 (1993), 1-3
MSC: Primary 20J05; Secondary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1993-1086347-3
MathSciNet review: 1086347
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Abstract: Consider $ 1 \to S \to E \to G \to 1$, where $ G$ is a finite $ p$-group generated by $ {g_i},\;1 \leqslant i \leqslant d$, and $ E$ a free product of cyclic groups $ \langle {g_i}\rangle ,1 \leqslant i \leqslant d$. If $ d$ is the minimum number of generators for $ G$, then we prove that the largest elementary abelian $ p$-quotient $ S/{S'}{S^p}$, regarded as an $ {\mathbb{F}_p}G$-module via conjugation in $ E$, is nonprojective and indecomposable.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1086347-3
Article copyright: © Copyright 1993 American Mathematical Society

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