ISOMORPHISMS OF PARTIAL GROUP RINGS
Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 161-168
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We consider the isomorphism problem for partial group rings $R_{\hbox{\scriptsize\it par}}G$ and show that, in the modular case, if $\textit{char}(R)\,{=}\,p$ and $R_{\hbox{\scriptsize\it par}}G_1\,{\cong}\, R_{\hbox{\scriptsize\it par}}G_2$ then the corresponding group rings of the Sylow $p$-subgroups are isomorphic. We use this to prove that finite abelian groups having isomorphic modular partial group algebras are isomorphic. Moreover, in the integral case, we show that the isomorphism of partial group rings of finite groups $G_1$ and $G_2$ implies $\Z G_1\,{\cong}\, \Z G_2$.
DOKUCHAEV, M. A.; MILIES, C. POLCINO. ISOMORPHISMS OF PARTIAL GROUP RINGS. Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 161-168. doi: 10.1017/S0017089503001630
@article{10_1017_S0017089503001630,
author = {DOKUCHAEV, M. A. and MILIES, C. POLCINO},
title = {ISOMORPHISMS {OF} {PARTIAL} {GROUP} {RINGS}},
journal = {Glasgow mathematical journal},
pages = {161--168},
year = {2004},
volume = {46},
number = {1},
doi = {10.1017/S0017089503001630},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001630/}
}
TY - JOUR AU - DOKUCHAEV, M. A. AU - MILIES, C. POLCINO TI - ISOMORPHISMS OF PARTIAL GROUP RINGS JO - Glasgow mathematical journal PY - 2004 SP - 161 EP - 168 VL - 46 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001630/ DO - 10.1017/S0017089503001630 ID - 10_1017_S0017089503001630 ER -
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