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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… Click to show full 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.
Keywords:
subnormal sylow;
finite groups;
sylow subgroups;
groups subnormal;
group
Journal Title: Ukrainian Mathematical Journal
Year Published: 2021
Link to full text (if available)
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Journal Title: Ukrainian Mathematical Journal
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!