Overgroups of elementary block-diagonal subgroups in the classical symplectic group over an arbitrary commutative ring

Standard

Overgroups of elementary block-diagonal subgroups in the classical symplectic group over an arbitrary commutative ring. / Shchegolev, A. V.

In: St. Petersburg Mathematical Journal, Vol. 30, No. 6, 01.01.2019, p. 1007-1041.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{2ba4dffb83454cb0ad2a7ee7cf71eeef,

title = "Overgroups of elementary block-diagonal subgroups in the classical symplectic group over an arbitrary commutative ring",

abstract = "The paper provides a sandwich classification theorem for subgroups of the classical symplectic group over an arbitrary commutative ring R that contain the elementary block-diagonal (or subsystem) subgroup Ep(ν,R) corresponding to a unitary equivalence relation ν such that all selfconjugate equivalence classes of ν are of size at least 4 and all nonselfconjugate classes of ν are of size at least 5. Namely, given a subgroup H ≥ Ep(ν,R) of Sp(2n,R), it is shown that there exists a unique exact major form net of ideals (σ, Γ) over R such that Ep(σ, Γ) ≤ H ≤ NSp(2n,R)(Sp(σ, Γ)). Next, the normalizer NSp(2n,R)(Sp(σ, Γ)) is described in terms of congruences.",

keywords = "Block-diagonal subgroup, Elementary subgroup, Localization methods, Standard automorphisms, Subgroup structure, Symplectic group, block-diagonal subgroup, subgroup structure, MAXIMAL-SUBGROUPS, standard automorphisms, elementary subgroup, localization methods",

author = "Shchegolev, {A. V.}",

year = "2019",

month = jan,

day = "1",

doi = "10.1090/spmj/1580",

language = "English",

volume = "30",

pages = "1007--1041",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "6",

}

RIS

TY - JOUR

T1 - Overgroups of elementary block-diagonal subgroups in the classical symplectic group over an arbitrary commutative ring

AU - Shchegolev, A. V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The paper provides a sandwich classification theorem for subgroups of the classical symplectic group over an arbitrary commutative ring R that contain the elementary block-diagonal (or subsystem) subgroup Ep(ν,R) corresponding to a unitary equivalence relation ν such that all selfconjugate equivalence classes of ν are of size at least 4 and all nonselfconjugate classes of ν are of size at least 5. Namely, given a subgroup H ≥ Ep(ν,R) of Sp(2n,R), it is shown that there exists a unique exact major form net of ideals (σ, Γ) over R such that Ep(σ, Γ) ≤ H ≤ NSp(2n,R)(Sp(σ, Γ)). Next, the normalizer NSp(2n,R)(Sp(σ, Γ)) is described in terms of congruences.

AB - The paper provides a sandwich classification theorem for subgroups of the classical symplectic group over an arbitrary commutative ring R that contain the elementary block-diagonal (or subsystem) subgroup Ep(ν,R) corresponding to a unitary equivalence relation ν such that all selfconjugate equivalence classes of ν are of size at least 4 and all nonselfconjugate classes of ν are of size at least 5. Namely, given a subgroup H ≥ Ep(ν,R) of Sp(2n,R), it is shown that there exists a unique exact major form net of ideals (σ, Γ) over R such that Ep(σ, Γ) ≤ H ≤ NSp(2n,R)(Sp(σ, Γ)). Next, the normalizer NSp(2n,R)(Sp(σ, Γ)) is described in terms of congruences.

KW - Block-diagonal subgroup

KW - Elementary subgroup

KW - Localization methods

KW - Standard automorphisms

KW - Subgroup structure

KW - Symplectic group

KW - block-diagonal subgroup

KW - subgroup structure

KW - MAXIMAL-SUBGROUPS

KW - standard automorphisms

KW - elementary subgroup

KW - localization methods

UR - http://www.scopus.com/inward/record.url?scp=85073721087&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=41712611

U2 - 10.1090/spmj/1580

DO - 10.1090/spmj/1580

M3 - Article

AN - SCOPUS:85073721087

VL - 30

SP - 1007

EP - 1041

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 6

ER -

ID: 48695263