TY - JOUR

T1 - Shunkov Groups Saturated with Almost Simple Groups

AU - Maslova, N. V.

AU - Shlepkin, A. A.

N1 - Supported by Russian Science Foundation, project No. 19-71-10017-P (Thm. 1). (A. A. Shlepkin). Supported by RFBR, project No. 20-01-00456 (Thm. 2). (N. V. Maslova).

PY - 2023/3/1

Y1 - 2023/3/1

N2 - A group G is called a Shunkov group (a conjugate biprimitive finite group) if, for any of its finite subgroups H in the factor group NG(H)/H, every two conjugate elements of prime order generate a finite subgroup. We say that a group is saturated with groups from the set R if any finite subgroup of the given group is contained in its subgroup isomorphic to some group in R. We show that a Shunkov group G which is saturated with groups from the set R possessing specific properties, and contains an involution z with the property that the centralizer CG(z) has only finitely many elements of finite order will have a periodic part isomorphic to one of the groups in R. In particular, a Shunkov group G that is saturated with finite almost simple groups and contains an involution z with the property that the centralizer CG(z) has only finitely many elements of finite order will have a periodic part isomorphic to a finite almost simple group.

AB - A group G is called a Shunkov group (a conjugate biprimitive finite group) if, for any of its finite subgroups H in the factor group NG(H)/H, every two conjugate elements of prime order generate a finite subgroup. We say that a group is saturated with groups from the set R if any finite subgroup of the given group is contained in its subgroup isomorphic to some group in R. We show that a Shunkov group G which is saturated with groups from the set R possessing specific properties, and contains an involution z with the property that the centralizer CG(z) has only finitely many elements of finite order will have a periodic part isomorphic to one of the groups in R. In particular, a Shunkov group G that is saturated with finite almost simple groups and contains an involution z with the property that the centralizer CG(z) has only finitely many elements of finite order will have a periodic part isomorphic to a finite almost simple group.

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U2 - 10.1007/s10469-023-09725-y

DO - 10.1007/s10469-023-09725-y

M3 - Article

VL - 62

SP - 66

EP - 71

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 1

ER -