http://dspace.nbuv.gov.ua:80/handle/123456789/188469 2026-04-22T14:32:35Z http://dspace.nbuv.gov.ua:80/handle/123456789/188509 On p-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups Trofimuk, A. Let G be a finite group and P be a p-subgroup of G. If P is a Sylow subgroup of some normal subgroup of G, then we say that P is normally embedded in G. Groups with normally embedded maximal subgroups of Sylow p-subgroup, where (|G|, p − 1) = 1, are studied. In particular, the p-nilpotency of such groups is proved. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188508 Sets of prime power order generators of finite groups Stocka, A. A subset X of prime power order elements of a finite group G is called pp-independent if there is no proper subset Y of X such that 〈Y,Ф(G)〉 = 〈X,Ф(G)〉, where Ф(G) is the Frattini subgroup of G. A group G has property Bpp if all pp-independent generating sets of G have the same size. G has the pp-basis exchange property if for any pp-independent generating sets B₁,B₂ of G and x ∈ B₁ there exists y ∈ B₂ such that (B₁ \ {x}) ∪ {y} is a pp-independent generating set of G. In this paper we describe all finite solvable groups with property Bpp and all finite solvable groups with the pp-basis exchange property. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188507 Linear groups saturated by subgroups of finite central dimension Semko, N.N.; Skaskiv, L.V.; Yarovaya, O.A. Let F be a field, A be a vector space over F and G be a subgroup of GL(F,A). We say that G has a dense family of subgroups, having finite central dimension, if for every pair of subgroups H, K of G such that H ≤ K and H is not maximal in K there exists a subgroup L of finite central dimension such that H ≤ L ≤ K. In this paper we study some locally soluble linear groups with a dense family of subgroups, having finite central dimension. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188506 On some non-periodic groups whose cyclic subgroups are GNA-subgroups Pypka, A A. In this paper we obtain the description of nonperiodic locally generalized radical groups whose cyclic subgroups are GNA-subgroups. 2020-01-01T00:00:00Z