TY - JOUR

T1 - On the Sharp Baer–Suzuki Theorem for the π-Radical: Sporadic Groups

AU - Yang, N.

AU - Wu, Zh

AU - Revin, D. O.

N1 - Funding Information: The work was supported by the Russian Science Foundation (Grant 19–11–00039). Zh. Wu was supported by the Natural Science Foundation of the Jiangsu Province, China (Grant no. BK20210442), and the Jiangsu Shuangchuang, Mass Innovation and Entrepreneurship, Talent Program (Grant no. JSSCBS20210841). Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/3

Y1 - 2022/3

N2 - Let ππ be a proper subset of the set of all primes and |π|≥2|π|≥2. Denote the smallest prime not in ππ by rr and let m=rm=r if r=2,3r=2,3, and m=r−1m=r−1 if r≥5r≥5. We study the following conjecture: A conjugacy class DD of a finite group GG lies in the ππ-radical Oπ(G)Oπ(G) of GG if and only if every mm elements of DD generate a ππ-subgroup. We confirm this conjecture for the groups GG whose every nonabelian composition factor is isomorphic to a sporadic or alternating group.

AB - Let ππ be a proper subset of the set of all primes and |π|≥2|π|≥2. Denote the smallest prime not in ππ by rr and let m=rm=r if r=2,3r=2,3, and m=r−1m=r−1 if r≥5r≥5. We study the following conjecture: A conjugacy class DD of a finite group GG lies in the ππ-radical Oπ(G)Oπ(G) of GG if and only if every mm elements of DD generate a ππ-subgroup. We confirm this conjecture for the groups GG whose every nonabelian composition factor is isomorphic to a sporadic or alternating group.

KW - 512.542

KW - Baer–Suzuki π-theorem

KW - sporadic simple group

KW - π-radical of a finite group

UR - http://www.scopus.com/inward/record.url?scp=85127780062&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/7be59585-8401-351d-b49a-fe5cde53c64f/

U2 - 10.1134/S0037446622020161

DO - 10.1134/S0037446622020161

M3 - Article

AN - SCOPUS:85127780062

VL - 63

SP - 387

EP - 394

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -