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Zapiski Nauchnykh Seminarov LOMI, 1979, Volume 94, Pages 21–36
(Mi znsl1801)
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This article is cited in 5 scientific papers (total in 5 papers)
Parabolic subgroups of twisted Chevalley groups over a semilocal ring
N. A. Vavilov
Abstract:
It is shown that, under minor additional assumptions, the standard parabolic subgroups of a Chevalley group $G_\rho(\Phi,R)$ of twisted type $\Phi=A_\ell$, $\ell$ – odd, $D_\ell$ ,$E_6$ over a commutative semilocal ring $R$ with involution $\rho$ are in one-to-one correspondence with the $\rho$-invariant parabolic nets of ideals of $R$ of type $\Phi$, i.e., with the sets, of ideals $\sigma_\alpha$ of $R$ such that: (1) whenever; (2) $\rho\sigma_\alpha=\sigma_{\rho\alpha}$ for all $\alpha$; (3 $\sigma_\alpha=R$ for $\alpha>0$. For Chevalley groups of normal types, analogous results were obtained in Ref. Zh. Mat. 1976, 10A151; 1977, 10A 301; 1978, 6A476.
Citation:
N. A. Vavilov, “Parabolic subgroups of twisted Chevalley groups over a semilocal ring”, Rings and modules. Part 2, Zap. Nauchn. Sem. LOMI, 94, "Nauka", Leningrad. Otdel., Leningrad, 1979, 21–36; J. Soviet Math., 19:1 (1982), 987–998
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https://www.mathnet.ru/eng/znsl1801 https://www.mathnet.ru/eng/znsl/v94/p21
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Abstract page: | 207 | Full-text PDF : | 63 |
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