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- Title
On the Existence of Hereditarily -Permutable Subgroups in Exceptional Groups of Lie Type.
- Authors
Galt, A. A.; Tyutyanov, V. N.
- Abstract
A subgroup of a group is -permutable in if for every subgroup there exists such that . A subgroup is hereditarily -permutable in if is -permutable in every subgroup of which includes . The Kourovka Notebook has Problem 17.112(b): Which finite nonabelian simple groups possess a proper hereditarily -permutable subgroup? We answer this question for the exceptional groups of Lie type. Moreover, for the Suzuki groups we prove that a proper subgroup of is -permutable if and only if the order of the subgroup is 2. In particular, we obtain an infinite series of groups with -permutable subgroups.
- Subjects
FINITE simple groups; NONABELIAN groups; INFINITE groups; INFINITE series (Mathematics)
- Publication
Siberian Mathematical Journal, 2023, Vol 64, Issue 5, p1110
- ISSN
0037-4466
- Publication type
Article
- DOI
10.1134/S003744662305004X