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Pregled bibliografske jedinice broj: 628760

On centralisers and normalisers for groups


Širola, Boris
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)


CROSBI ID: 628760 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

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:

Avatar Url Boris Širola (autor)

Poveznice na cjeloviti tekst rada:

doi journals.cambridge.org

Citiraj ovu publikaciju:

Širola, Boris
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)
Širola, B. (2012) On centralisers and normalisers for groups. Bulletin of the Australian Mathematical Society, 86 (3), 481-494 doi:10.1017/S0004972712000548.
@article{article, author = {\v{S}irola, Boris}, year = {2012}, pages = {481-494}, DOI = {10.1017/S0004972712000548}, keywords = {centraliser, normaliser, self-normalising subgroup, parabolic subgroup}, journal = {Bulletin of the Australian Mathematical Society}, doi = {10.1017/S0004972712000548}, volume = {86}, number = {3}, issn = {0004-9727}, title = {On centralisers and normalisers for groups}, keyword = {centraliser, normaliser, self-normalising subgroup, parabolic subgroup} }
@article{article, author = {\v{S}irola, Boris}, year = {2012}, pages = {481-494}, DOI = {10.1017/S0004972712000548}, keywords = {centraliser, normaliser, self-normalising subgroup, parabolic subgroup}, journal = {Bulletin of the Australian Mathematical Society}, doi = {10.1017/S0004972712000548}, volume = {86}, number = {3}, issn = {0004-9727}, title = {On centralisers and normalisers for groups}, keyword = {centraliser, normaliser, self-normalising subgroup, parabolic subgroup} }

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


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