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Zapiski Nauchnykh Seminarov POMI, 1999, Volume 265, Pages 163–168 (Mi znsl1195)  
Decomposition of Grothendieck group of stable categories of finite groups

A. I. Generalov, I. O. Isametdinov

Saint-Petersburg State University
Full-text PDF (162 kB)
Abstract: Let $G$ be a finite group with a normal Sylow $p$-subgroup $H$ such that the corresponding quotient is abelian. We prove that the Grothendieck group of the stable category of $G$ (over an algebraically closed field with characteristic $p$) contains a cyclic direct summand of order $|H|$.
Received: 25.12.1999
English version:
Journal of Mathematical Sciences (New York), 2002, Volume 112, Issue 4, Pages 4333–4336
DOI: https://doi.org/10.1023/A:1020390818802
Bibliographic databases:
UDC: 512.6
Language: Russian
Citation: A. I. Generalov, I. O. Isametdinov, “Decomposition of Grothendieck group of stable categories of finite groups”, Problems in the theory of representations of algebras and groups. Part 6, Zap. Nauchn. Sem. POMI, 265, POMI, St. Petersburg, 1999, 163–168; J. Math. Sci. (New York), 112:4 (2002), 4333–4336
Citation in format AMSBIB
\Bibitem{GenIsa99}
\by A.~I.~Generalov, I.~O.~Isametdinov
\paper Decomposition of Grothendieck group of stable categories of finite groups
\inbook Problems in the theory of representations of algebras and groups. Part~6
\serial Zap. Nauchn. Sem. POMI
\yr 1999
\vol 265
\pages 163--168
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1195}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1757821}
\zmath{https://zbmath.org/?q=an:1046.19001}
\transl
\jour J. Math. Sci. (New York)
\yr 2002
\vol 112
\issue 4
\pages 4333--4336
\crossref{https://doi.org/10.1023/A:1020390818802}
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