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Finite Groups with ℙ-Subnormal Sylow Subgroups.
- Source :
-
Ukrainian Mathematical Journal . Mar2021, Vol. 72 Issue 10, p1571-1578. 8p. - Publication Year :
- 2021
-
Abstract
- Let ℙ be the set of all prime numbers. A subgroup H of a finite group G is called ℙ-subnormal if either H = G or there exists a chain of subgroups H = H0 ≤ H1 ≤ ... ≤ Hn = G such that |Hi : Hi − 1| ∈ ℙ, 1 ≤ i ≤ n. We prove that any finite group with ℙ-subnormal Sylow p-subgroup of odd order is p-solvable and any group with ℙ-subnormal generalized Schmidt subgroups is metanilpotent. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SYLOW subgroups
*FINITE groups
*PRIME numbers
Subjects
Details
- Language :
- English
- ISSN :
- 00415995
- Volume :
- 72
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Ukrainian Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 150539161
- Full Text :
- https://doi.org/10.1007/s11253-021-01872-8