TY - JOUR

T1 - Groups with bounded centralizer chains and the Borovik-Khukhro conjecture

AU - Buturlakin, Alexander A.

AU - Revin, Danila O.

AU - Vasil'Ev, Andrey V.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - Let G be a locally finite group and let F.G/ be the Hirsch-Plotkin radical of G. Let S denote the full inverse image of the generalized Fitting subgroup of G=F.G/ in G. Assume that there is a number k such that the length of every nested chain of centralizers in G does not exceed k. The Borovik-Khukhro conjecture states, in particular, that under this assumption, the quotient G=S contains an abelian subgroup of finite index bounded in terms of k. We disprove this statement and prove a weak analogue of it.

AB - Let G be a locally finite group and let F.G/ be the Hirsch-Plotkin radical of G. Let S denote the full inverse image of the generalized Fitting subgroup of G=F.G/ in G. Assume that there is a number k such that the length of every nested chain of centralizers in G does not exceed k. The Borovik-Khukhro conjecture states, in particular, that under this assumption, the quotient G=S contains an abelian subgroup of finite index bounded in terms of k. We disprove this statement and prove a weak analogue of it.

KW - FINITE SIMPLE-GROUPS

KW - PERMUTATION-GROUPS

KW - MINIMAL-CONDITION

KW - DIMENSION

KW - ELEMENTS

UR - http://www.scopus.com/inward/record.url?scp=85050675506&partnerID=8YFLogxK

U2 - 10.1515/jgth-2018-0026

DO - 10.1515/jgth-2018-0026

M3 - Article

AN - SCOPUS:85050675506

VL - 21

SP - 1095

EP - 1110

JO - Journal of Group Theory

JF - Journal of Group Theory

SN - 1433-5883

IS - 6

ER -