0000000000395668
AUTHOR
Lev Kazarin
showing 10 related works from this author
ON SYLOW NORMALIZERS OF FINITE GROUPS
2013
[EN] The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent Hall subgroups for given sets of primes are exactly the subgroup- closed saturated formations satisfying the following property: a group belongs to the class if and only if its Sylow normalizers do so. The paper analyzes the extension of this research to the universe of all finite groups.
Criteria for the solubility and non-simplicity of finite groups
2005
Abstract Some criteria of the non-simplicity of a finite group by graph theoretical terms are derived. This is then used to establish conditions under which a finite group is soluble.
On the product of a π-group and a π-decomposable group
2007
[EN] The main result in the paper states the following: Let π be a set of odd primes. Let the finite group G=AB be the product of a π -decomposable subgroup A=Oπ(A)×Oπ′(A) and a π -subgroup B . Then Oπ(A)⩽Oπ(G); equivalently the group G possesses Hall π -subgroups. In this case Oπ(A)B is a Hall π-subgroup of G. This result extends previous results of Berkovich (1966), Rowley (1977), Arad and Chillag (1981) and Kazarin (1980) where stronger hypotheses on the factors A and B of the group G were being considered. The results under consideration in the paper provide in particular criteria for the existence of non-trivial soluble normal subgroups for a factorized group G.
On the Soluble Graph of a Finite Simple Group
2013
The maximal independent sets of the soluble graph of a finite simple group G are studied and their independence number is determined. In particular, it is shown that this graph in many cases has an independent set with three vertices.
On the product of a nilpotent group and a group with non-trivial center
2007
Abstract It is proved that a finite group G = A B which is a product of a nilpotent subgroup A and a subgroup B with non-trivial center contains a non-trivial abelian normal subgroup.
A reduction theorem for a conjecture on products of two π -decomposable groups
2013
[EN] For a set of primes pi, a group X is said to be pi-decomposable if X = X-pi x X-pi' is the direct product of a pi-subgroup X-pi and a pi'-subgroup X-pi', where pi' is the complementary of pi in the set of all prime numbers. The main result of this paper is a reduction theorem for the following conjecture: "Let pi be a set of odd primes. If the finite group G = AB is a product of two pi-decomposable subgroups A = A(pi) x A(pi') and B = B-pi x B-pi', then A(pi)B(pi) = B(pi)A(pi) and this is a Hall pi-subgroup of G." We establish that a minimal counterexample to this conjecture is an almost simple group. The conjecture is then achieved in a forthcoming paper. (C) 2013 Elsevier Inc. All ri…
On finite products of soluble groups
1998
Let the finite groupG =AB be the product of two soluble subgroupsA andB, and letπ be a set of primes. We investigate under which conditions for the maximal normalπ-subgroups ofA, B andG the following holds:Oπ(G) ∩Oπ(G) ⊆Oπ(G).
FINITE TRIFACTORISED GROUPS AND -DECOMPOSABILITY
2018
We derive some structural properties of a trifactorised finite group $G=AB=AC=BC$, where $A$, $B$, and $C$ are subgroups of $G$, provided that $A=A_{\unicode[STIX]{x1D70B}}\times A_{\unicode[STIX]{x1D70B}^{\prime }}$ and $B=B_{\unicode[STIX]{x1D70B}}\times B_{\unicode[STIX]{x1D70B}^{\prime }}$ are $\unicode[STIX]{x1D70B}$-decomposable groups, for a set of primes $\unicode[STIX]{x1D70B}$.
Products of locally dihedral subgroups
2012
AbstractIt is shown that a group G=AB which is a product of two periodic locally dihedral subgroups A and B is soluble.
Large subgroups of a finite group of even order
2011
It is shown that if G G is a group of even order with trivial center such that | G | > 2 | C G ( t ) | 3 |G|>2|C_{G}(t)|^{3} for some involution t ∈ G t\in G , then there exists a proper subgroup H H of G G such that | G | > | H | 2 |G|> |H|^{2} . If | G | > | C G ( t ) | 3 |G|>|C_{G}(t)|^{3} and k ( G ) k(G) is the class number of G G , then | G | ≤ k ( G ) 3 |G|\leq k(G)^{3} .