Pregled bibliografske jedinice broj: 542188
Normalizers and self-normalizing subgoups II
Normalizers and self-normalizing subgoups II // Central European Journal of Mathematics, 9 (2011), 6; 1317-1332 doi:10.2478/s11533-011-0091-2 (međunarodna recenzija, članak, znanstveni)
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Naslov
Normalizers and self-normalizing subgoups II
(Normalizers and self-normalizing subgroups II)
Autori
Širola, Boris
Izvornik
Central European Journal of Mathematics (1895-1074) 9
(2011), 6;
1317-1332
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Normalizer; self-normalizing subgroup; centralizer; symplectic group; even orthogonal group; odd orthogonal group
Sažetak
Let $\mathbb K$ be a field, $\boldsymbol{; ; G}; ; $ a reductive algebraic $\mathbb K$-group, and $\boldsymbol{; ; G}; ; _1\leq \boldsymbol{; ; G}; ; $ a reductive subgroup. For $G_1\leq G$, the corresponding groups of $\mathbb K$-points, we study the normalizer $\mathsf{; ; N}; ; =\mathcal N_G(G_1)$. In particular, for a standard embedding of the odd orthogonal group $G_1={; ; \rm SO}; ; (m, \mathbb K)$ in $G={; ; \rm SL}; ; (m, \mathbb K)$ we have that $\mathsf{; ; N}; ; $ is isomorphic to the semidirect product of $G_1$ by $\boldsymbol{; ; \mu}; ; _{; ; m}; ; (\mathbb K)$, the group of $m$-th roots of unity in $\mathbb K$. The normalizers of the even orthogonal and symplectic subgroup of ${; ; \rm SL}; ; (2n, \mathbb K)$ were computed in [B. \v S., {; ; \it Normalizers and self-normalizing subgroups}; ; ], leaving the proof in the odd orthogonal case to be completed here. Also, for $G={; ; \rm GL}; ; (m, \mathbb K)$ and $G_1={; ; \rm O}; ; (m, \mathbb K)$ we have that $\mathsf{; ; N}; ; $ is isomorphic to the semidirect product of $G_1$ by $\mathbb K^{; ; \times}; ; $. In both of these cases, $\mathsf{; ; N}; ; $ is a self-normalizing subgroup of $G$.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
037-0372781-2811 - Omotačke algebre Liejevih algebri i njihovi moduli (Širola, Boris, MZOS ) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb
Profili:
Boris Širola
(autor)
Citiraj ovu publikaciju:
Časopis indeksira:
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
Uključenost u ostale bibliografske baze podataka::
- MathSciNet
- Zentrallblatt für Mathematik/Mathematical Abstracts