Pregled bibliografske jedinice broj: 628760
On centralisers and normalisers for groups
On centralisers and normalisers for groups // Bulletin of the Australian Mathematical Society, 86 (2012), 3; 481-494 doi:10.1017/S0004972712000548 (međunarodna recenzija, članak, znanstveni)
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Naslov
On centralisers and normalisers for groups
Autori
Širola, Boris
Izvornik
Bulletin of the Australian Mathematical Society (0004-9727) 86
(2012), 3;
481-494
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
centraliser; normaliser; self-normalising subgroup; parabolic subgroup
Sažetak
Let K be a field, $char(K)\neq 2$, and G a subgroup of GL(n, K). Suppose $g\mapsto g^{; ; \sharp}; ; $ is a K-linear antiautomorphism of G, and then define $G_1={; ; g\in G|g^{; ; \sharp}; ; g=I}; ; $. For C being the centraliser $C_G(G_1)$, or any subgroup of the centre Z(G), define $G^{; ; (C)}; ; ={; ; g\in G|g^{; ; \sharp}; ; g\in C}; ; $. We show that $G^{; ; (C)}; ; $ is a subgroup of G, and study its structure. When $C=C_G(G_1)$, we have that $G^{; ; (C)}; ; =N_G(G_1)$, the normaliser of $G_1$ in G. Suppoe K is algebraically closed, $C_G(G_1)$ consists of scalar matrices and $G_1$ is a connected subgroup of an affine group G. Under the latter assumptions, $N_G(G_1)$ is a self-normalising subgroup of G. This holds for a number of interesting pairs $(G, G_1)$ ; in particular, for those that we call parabolic pairs. As well, for a certain specific setting we generalise a standard result about centres of Borel subgroups.
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