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https://doi.org/10.3336/gm.46.2.10

Normalizers and self-normalizing subgroups

Boris Sirola ; Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Puni tekst: engleski, pdf (307 KB) str. 385-414 preuzimanja: 322* citiraj
APA 6th Edition
Sirola, B. (2011). Normalizers and self-normalizing subgroups. Glasnik matematički, 46 (2), 385-414. https://doi.org/10.3336/gm.46.2.10
MLA 8th Edition
Sirola, Boris. "Normalizers and self-normalizing subgroups." Glasnik matematički, vol. 46, br. 2, 2011, str. 385-414. https://doi.org/10.3336/gm.46.2.10. Citirano 24.10.2020.
Chicago 17th Edition
Sirola, Boris. "Normalizers and self-normalizing subgroups." Glasnik matematički 46, br. 2 (2011): 385-414. https://doi.org/10.3336/gm.46.2.10
Harvard
Sirola, B. (2011). 'Normalizers and self-normalizing subgroups', Glasnik matematički, 46(2), str. 385-414. https://doi.org/10.3336/gm.46.2.10
Vancouver
Sirola B. Normalizers and self-normalizing subgroups. Glasnik matematički [Internet]. 2011 [pristupljeno 24.10.2020.];46(2):385-414. https://doi.org/10.3336/gm.46.2.10
IEEE
B. Sirola, "Normalizers and self-normalizing subgroups", Glasnik matematički, vol.46, br. 2, str. 385-414, 2011. [Online]. https://doi.org/10.3336/gm.46.2.10

Sažetak
Let K be a field, char(K) ≠ 2. Suppose G=G(K) is the group of K-points of a reductive algebraic K-group G. Let G1≤ G be the group of K-points of a reductive subgroup G1≤ G. We study the structure of the normalizer N= NG(G1). In particular, let G= SL(2n, K) for n>1. For certain well known embeddings of G1 into G, where G1= Sp(2n, K) or SO(2n, K), we show that N/G1 ≅ μk(K), the group of k-th roots of unity in K. Here, k=2n if certain Condition (◊) holds, and k=n if not. Moreover, there is a precisely defined subgroup N' of N such that N/N' ≅ Z/2 Z if Condition (◊) holds, and N=N' if not. Furthermore, when n>1, as the main observations of the paper we have the following: (i) N is a self-normalizing subgroup of G; (ii) N' ≅ G1Z[X] μn (K), the semidirect product of G1 by μn (K). Besides we point out that analogous results will hold for a number of other pairs of groups (G,G1). We also show that for the pair (g, g1), of the corresponding K-Lie algebras, g1 is self-normalizing in g; which generalizes a well-known result in the zero characteristic.

Ključne riječi
Normalizer; self-normalizing subgroup; symmetric pair; symplectic group; even orthogonal group

Hrčak ID: 74268

URI
https://hrcak.srce.hr/74268

Posjeta: 533 *