On p-solvability of finite groups. (Russian) Zbl 0592.20031
Arithmetical and subgroup construction of finite groups, Collect. Artic., Minsk 1986, 3-7 (1986).
[For the entire collection see Zbl 0591.00008.]
Main result. Let \(P\in Syl_ p(G)\), \(p>2\), and every subgroup \(P_ k\leq P\), \(| P_ k| =p^ k\), is permutable with \(Q\in Syl(G)\), \((| Q|,p)=1\). Then G is p-solvable of p-length 1.
Main result. Let \(P\in Syl_ p(G)\), \(p>2\), and every subgroup \(P_ k\leq P\), \(| P_ k| =p^ k\), is permutable with \(Q\in Syl(G)\), \((| Q|,p)=1\). Then G is p-solvable of p-length 1.
Reviewer: Ya.G.Berkovich
MSC:
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
