@article{77d61c0d93c448fa8fe4d84e4d4a95bc,
title = "On the Sharp Baer–Suzuki Theorem for the π-Radical: Sporadic Groups",
abstract = "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.",
keywords = "512.542, Baer–Suzuki π-theorem, sporadic simple group, π-radical of a finite group",
author = "N. Yang and Zh Wu and Revin, {D. O.}",
note = "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: {\textcopyright} 2022, Pleiades Publishing, Ltd.",
year = "2022",
month = mar,
doi = "10.1134/S0037446622020161",
language = "English",
volume = "63",
pages = "387--394",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "2",
}