Search results for "Permutable prime"
showing 10 items of 19 documents
Maximal subgroups and PST-groups
2013
A subgroup H of a group G is said r to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maxmial subgroups, Arch. Math. (Basel), 2011, 96(1), 19-25)] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions o…
Products of pairwise totally permutable groups
2003
[EN] In this paper finite groups factorized as products of pairwise totally permutable subgroups are studied in the framework of Fitting classes
On mutually permutable products of finite groups
2005
Abstract In this paper a structural theorem about mutually permutable products of finite groups is obtained. This result is used to derive some results on mutually permutable products of groups whose chief factors are simple. Some earlier results on mutually permutable products of supersoluble groups appear as particular cases.
On totally permutable products of finite groups
2005
[EN] The behaviour of totally permutable products of finite groups with respect to certain classes of groups is studied in the paper. The results are applied to obtain information about totally permutable products of T, PT, and PST-groups.
On finite products of totally permutable groups
1996
In this paper the structure of finite groups which are the product of two totally permutable subgroups is studied. In fact we can obtain the -residual, where is a formation, -projectors and -normalisers, where is a saturated formation, of the group from the corresponding subgroups of the factor subgroups.
Fitting classes and products of totally permutable groups
2002
The second and third authors have been supported by Proyecto PB 97-0674-C02-02 of DGESIC, Ministerio de Educación y Cultura, Spain.
On finite products of groups and supersolubility
2010
Two subgroups X and Y of a group G are said to be conditionally permutable in G if X permutes with Y(g) for some element g E G. i.e., XY(g) is a subgroup of G. Using this permutability property new criteria for the product of finite supersoluble groups to be supersoluble are obtained and previous results are recovered. Also the behaviour of the supersoluble residual in products of finite groups is studied.
Saturated formations and products of connected subgroups
2011
Abstract For a non-empty class of groups C , two subgroups A and B of a group G are said to be C -connected if 〈 a , b 〉 ∈ C for all a ∈ A and b ∈ B . Given two sets π and ρ of primes, S π S ρ denotes the class of all finite soluble groups that are extensions of a normal π-subgroup by a ρ-group. It is shown that in a finite group G = A B , with A and B soluble subgroups, then A and B are S π S ρ -connected if and only if O ρ ( B ) centralizes A O π ( G ) / O π ( G ) , O ρ ( A ) centralizes B O π ( G ) / O π ( G ) and G ∈ S π ∪ ρ . Moreover, if in this situation A and B are in S π S ρ , then G is in S π S ρ . This result is then extended to a large family of saturated formations F , the so-c…
Injectors and Radicals in Products of Totally Permutable Groups
2003
Abstract Two subgroups H and K of a group G are said to be totally permutable if every subgroup of H permutes with every subgroup of K. In this paper the behaviour of radicals and injectors associated to Fitting classes in a product of pairwise totally permutable finite groups is studied.
Permutability in finite soluble groups
1994
Let G be a finite soluble group and let Σ be a Hall system of G. A subgroup U of G is said to be Σ-permutable if U permutes with every member of Σ. In [1; I, 4·29] it is proved that if U and V are Σ-permutable subgroups of G then so also are U ∩ V and 〈U, V〉.