Serial Group Rings of Finite Groups. p-nilpotency

It is proved that if F is an arbitrary field of characteristic p and G is a finite p-nilpotent group with a cyclic p-Sylow subgroup, then the group ring FG is serial. As a corollary, it is shown that for an arbitrary field F of characteristic 2 and any finite group G, the ring FG is serial if and on...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2014-10, Vol.202 (3), p.422-433
Main Authors: Kukharev, A. V., Puninski, G. E.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:It is proved that if F is an arbitrary field of characteristic p and G is a finite p-nilpotent group with a cyclic p-Sylow subgroup, then the group ring FG is serial. As a corollary, it is shown that for an arbitrary field F of characteristic 2 and any finite group G, the ring FG is serial if and only if the 2-Sylow subgroup of G is cyclic.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-014-2052-3