TY - JOUR

T1 - The Strong -Sylow Theorem for the Groups PSL

AU - Revin, D. O.

AU - Shepelev, V. D.

PY - 2024/9/25

Y1 - 2024/9/25

N2 - Let be a set of primes. A finite group is a -group if allprime divisors of the order of belong to. Following Wielandt,the -Sylow theorem holds for if all maximal-subgroups of are conjugate; if the -Sylow theorem holds forevery subgroup of then the strong -Sylow theorem holdsfor. The strong -Sylow theorem is known to hold for if and only if it holds for every nonabelian composition factor of.In 1979, Wielandt asked which finite simple nonabelian groups obey the strong -Sylow theorem.By now the answer isknown for sporadic and alternating groups. We give somearithmetic criterion for the validity of the strong -Sylow theorem forthe groups.

AB - Let be a set of primes. A finite group is a -group if allprime divisors of the order of belong to. Following Wielandt,the -Sylow theorem holds for if all maximal-subgroups of are conjugate; if the -Sylow theorem holds forevery subgroup of then the strong -Sylow theorem holdsfor. The strong -Sylow theorem is known to hold for if and only if it holds for every nonabelian composition factor of.In 1979, Wielandt asked which finite simple nonabelian groups obey the strong -Sylow theorem.By now the answer isknown for sporadic and alternating groups. We give somearithmetic criterion for the validity of the strong -Sylow theorem forthe groups.

KW - -Sylow theorem

KW - 512.542

KW - projective special linear group

KW - strong -Sylow theorem

UR - https://www.mendeley.com/catalogue/d880aedd-19e0-3815-be2f-7b57297b1e87/

U2 - 10.1134/S0037446624050173

DO - 10.1134/S0037446624050173

M3 - Article

VL - 65

SP - 1187

EP - 1194

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -