TY - JOUR

T1 - Towards the Sharp Baer–Suzuki Theorem for the π-radical: Symplectic Groups

AU - Ревин, Данила Олегович

N1 - Revin, D.O. Towards the Sharp Baer–suzuki Theorem for the π-radical: Symplectic Groups. Algebra Logic 64, 379–396 (2025). https://doi.org/10.1007/s10469-026-09841-5 The research was carried out under the support of the Russian Science Foundation Grant No. 24-11-00127, https://rscf.ru/en/project/24-11-00127/.

PY - 2025/11

Y1 - 2025/11

N2 - We study the following conjecture, which is a sharp analogue of the well-known Baer–Suzuki theorem for the π-radical of a finite group. For an arbitrary set π of primes not containing all primes, let r be the smallest prime not in π. Set m = r if r ⩽ 3 and m = r − 1 if r > 3. Then, in a finite group G, the largest normal π-subgroup always coincides with the set of elements x such that any m conjugates of x generate a π-subgroup. To date, this conjecture has been confirmed for any finite group whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, or unitary simple group, or to one of the groups 2B2(q), 2G2(q), 2F4(q)′, G2(q), or 3D4(q). It is proved that the simple symplectic groups S2n(q) can be added to this list.

AB - We study the following conjecture, which is a sharp analogue of the well-known Baer–Suzuki theorem for the π-radical of a finite group. For an arbitrary set π of primes not containing all primes, let r be the smallest prime not in π. Set m = r if r ⩽ 3 and m = r − 1 if r > 3. Then, in a finite group G, the largest normal π-subgroup always coincides with the set of elements x such that any m conjugates of x generate a π-subgroup. To date, this conjecture has been confirmed for any finite group whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, or unitary simple group, or to one of the groups 2B2(q), 2G2(q), 2F4(q)′, G2(q), or 3D4(q). It is proved that the simple symplectic groups S2n(q) can be added to this list.

KW - finite simple symplectic group

KW - π-Baer–Suzuki theorem

KW - π-radical

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105045509694&origin=inward

UR - https://www.mendeley.com/catalogue/d8b158b0-1ecd-39f6-8ef0-6df6cf12b338/

U2 - 10.1007/s10469-026-09841-5

DO - 10.1007/s10469-026-09841-5

M3 - Article

VL - 64

SP - 379

EP - 396

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 5

ER -