Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102113
Title: On the pronormality of subgroups of odd index in finite simple symplectic groups
Authors: Kondrat’ev, A. S.
Maslova, N. V.
Revin, D. O.
Issue Date: 2017
Publisher: Springer New York LLC
Citation: Kondrat’ev A. S. On the pronormality of subgroups of odd index in finite simple symplectic groups / A. S. Kondrat’ev, N. V. Maslova, D. O. Revin. — DOI 10.1134/S0037446617030107 // Siberian Mathematical Journal. — 2017. — Vol. 58. — Iss. 3. — P. 467-475.
Abstract: A subgroup H of a group G is pronormal if the subgroups H and Hg are conjugate in 〈H,Hg〉 for every g ∈ G. It was conjectured in [1] that a subgroup of a finite simple group having odd index is always pronormal. Recently the authors [2] verified this conjecture for all finite simple groups other than PSLn(q), PSUn(q), E6(q), 2E6(q), where in all cases q is odd and n is not a power of 2, and P Sp2n(q), where q ≡ ±3 (mod 8). However in [3] the authors proved that when q ≡ ±3 (mod 8) and n ≡ 0 (mod 3), the simple symplectic group P Sp2n(q) has a nonpronormal subgroup of odd index, thereby refuted the conjecture on pronormality of subgroups of odd index in finite simple groups. The natural extension of this conjecture is the problem of classifying finite nonabelian simple groups in which every subgroup of odd index is pronormal. In this paper we continue to study this problem for the simple symplectic groups P Sp2n(q) with q ≡ ±3 (mod 8) (if the last condition is not satisfied, then subgroups of odd index are pronormal). We prove that whenever n is not of the form 2m or 2m(22k+1), this group has a nonpronormal subgroup of odd index. If n = 2m, then we show that all subgroups of P Sp2n(q) of odd index are pronormal. The question of pronormality of subgroups of odd index in P Sp2n(q) is still open when n = 2m(22k + 1) and q ≡ ±3 (mod 8). © 2017, Pleiades Publishing, Ltd.
Keywords: FINITE GROUP
ODD INDEX
PRONORMAL SUBGROUP
SIMPLE GROUP
SYMPLECTIC GROUP
URI: http://hdl.handle.net/10995/102113
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85021277265
PURE ID: 1926918
ISSN: 374466
DOI: 10.1134/S0037446617030107
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

Files in This Item:
File Description SizeFormat 
2-s2.0-85021277265.pdf232,16 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.