Search results for "Soluble groups"
showing 5 items of 5 documents
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…
Finite groups with subgroups supersoluble or subnormal
2009
Abstract The aim of this paper is to study the structure of finite groups whose non-subnormal subgroups lie in some subclasses of the class of finite supersoluble groups.
Some results on locally finite groups
2017
En esta tesis se presentan algunos resultados sobre p-nilpotencia y permutabilidad en grupos localmente finitos. Está estructurada en cinco capítulos. El primer capítulo, que tiene carácter introductorio: contiene definiciones y resultados conocidos que serán utilizados en los capítulos sucesivos. Por tratarse de resultados ya conocidos, se introducen con referencias y sin demostraciones. En el capítulo 2 se trata la p-nilpotencia en grupos hiperfinitos, donde p es un primo. Los resultados presentados se encuentran publicados en el siguiente artículo: Ballester-Bolinches, A.; Camp-Mora, S.; Spagnuolo, F., "On p-nilpotency of hyperfinite groups". Monatshefte f¨ur Mathematik, 176, no. 4, 497–…
On minimal non-supersoluble groups
2007
[EN] The aim of this paper is to classify the finite minimal non-p-supersoluble groups, p a prime number, in the p-soluble universe.
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.