TY - JOUR

T1 - Recognition of symplectic and orthogonal groups of small dimensions by spectrum

AU - Grechkoseeva, Mariya A.

AU - Vasil'Ev, Andrey V.

AU - Zvezdina, Mariya A.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - We refer to the set of the orders of elements of a finite group as its spectrum and say that finite groups are isospectral if their spectra coincide. In this paper, we determine all finite groups isospectral to the simple groups S6(q), O7(q), and O8+(q). In particular, we prove that with just four exceptions, every such finite group is an extension of the initial simple group by a (possibly trivial) field automorphism.

AB - We refer to the set of the orders of elements of a finite group as its spectrum and say that finite groups are isospectral if their spectra coincide. In this paper, we determine all finite groups isospectral to the simple groups S6(q), O7(q), and O8+(q). In particular, we prove that with just four exceptions, every such finite group is an extension of the initial simple group by a (possibly trivial) field automorphism.

KW - orders of elements

KW - recognition by spectrum

KW - Simple classical group

KW - FINITE SIMPLE-GROUPS

KW - ELEMENTS

KW - EXTENSIONS

KW - RECOGNIZABILITY

KW - ORDERS

KW - SIMPLE EXCEPTIONAL GROUPS

UR - http://www.scopus.com/inward/record.url?scp=85060727702&partnerID=8YFLogxK

U2 - 10.1142/S021949881950230X

DO - 10.1142/S021949881950230X

M3 - Article

AN - SCOPUS:85060727702

VL - 18

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

IS - 12

M1 - 1950230

ER -