Let A act on a group G. A is said to act p-cyclically on G if AN p A p-1 acts stably on G/O
p′(G), and A is said to act cyclically on G if A acts p-cyclically on G for all primes p. In this …

Let G be an A-group and let f be a formation function. Note that A is said to act f-
hypercentrally on G if A/C_A(H/K)∈f(p) on every A-composition factor H/K of G for all …

In this note, we prove that a finite group G is p-supersolvable if and only if there exists a
power d of p with p^2≦d<|P| such that H∩O^p(G^*_p) is normal in O^p(G) for all non-cyclic …

Пусть G A-группа и f формационная функция. Говорят, что A действует f-
гиперцентрально на G, если A/CA (H/K)∈ f (p) для любого A-композиционного фактора …

Пусть $ G $$ A $-группа и $ f $ формационная функция. Говорят, что $ A $ действует $ f
$-гиперцентрально на $ G $, если $ A/C_A (H/K)\in f (p) $ для любого $ A …

Let a finite group A act on a finite p-group P with| P|> pe, where e is an integer with e≥ 2. In
this paper, we show that P is centralized by O p (A up− 1) if every non-maximal class p …