Search results for "T-group"
showing 10 items of 14 documents
A class of generalised finite T-groups
2011
Let F be a formation (of finite groups) containing all nilpotent groups such that any normal subgroup of any T-group in F and any subgroup of any soluble T-group in F belongs to F. A subgroup M of a finite group G is said to be F-normal in G if G/CoreG(M) belongs to F. Named after Kegel, a subgroup U of a finite group G is called a K- F-subnormal subgroup of G if either U=G or U=U0?U1???Un=G such that Ui?1 is either normal in Ui or Ui1 is F-normal in Ui, for i=1,2,...,n. We call a finite group G a TF-group if every K- F-subnormal subgroup of G is normal in G. When F is the class of all finite nilpotent groups, the TF-groups are precisely the T-groups. The aim of this paper is to analyse the…
On a class of supersoluble groups
2014
A subgroup H of a finite group G is said to be S-semipermutable in G if H permutes with every Sylow q-subgroup of G for all primes q not dividing |H|. A finite group G is an MS-group if the maximal subgroups of all the Sylow subgroups of G are S-semipermutable in G. The aim of the present paper is to characterise the finite MS-groups.
Primitive subgroups and PST-groups
2014
AbstractAll groups considered in this paper are finite. A subgroup $H$ of a group $G$ is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of $G$ containing $H$ as a proper subgroup. He et al. [‘A note on primitive subgroups of finite groups’, Commun. Korean Math. Soc. 28(1) (2013), 55–62] proved that every primitive subgroup of $G$ has index a power of a prime if and only if $G/ \Phi (G)$ is a solvable PST-group. Let $\mathfrak{X}$ denote the class of groups $G$ all of whose primitive subgroups have prime power index. It is established here that a group $G$ is a solvable PST-group if and only if every subgroup of $G$ is an $\mathfrak{X}$-group.
Groups whose subgroups satisfy the weak subnormalizer condition
2019
A subgroup X of a group G is said to satisfy the weak subnormalizer condition if $$N_G(Y)\le N_G(X)$$ for each non-normal subgroup Y of G such that $$X\le Y\le N_G(X)$$ . The behaviour of generalized soluble groups whose (cyclic) subgroups satisfy the weak subnormalizer condition is investigated.
In-group favouritism and out-group derogation towards national groups: Age-related differences among Italian school children
2013
Abstract Recently many researchers investigated intergroup attitudes among children, but only few studies analyzed developmental pathways of in-group favouritism and out-group derogation in considerable samples across broad age ranges. The present study aims at examining age-related differences in in-group favouritism and out-group derogation towards national groups among Italian children. Six hundred-seven children (305 males, 302 females), aged 6–12 living in Italy, were asked to answer an individual interview, making various evaluations of the national in-group and of 2 salient national out-groups (German and English). For research purposes 3 measures were used: number of positive traits…
On self-normalising subgroups of finite groups
2010
[EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) in their normal, permutable, or S-permutable closure, respectively.
Some local properties defining $\mathcal T_0$-groups and related classes of groups
2016
We call $G$ a $\operatorname{Hall}_{\mathcal X}$-group if there exists a normal nilpotent subgroup $N$ of $G$ for which $G/N'$ is an ${\mathcal X}$-group. We call $G$ a ${\mathcal T}_0$-group provided $G/\Phi(G)$ is a ${\mathcal T}$-group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define $\operatorname{Hall}_{\mathcal X}$-groups and ${\mathcal T}_0$-groups where ${\mathcal X}\in\{ {\mathcal T},\mathcal {PT},\mathcal {PST}\}$; the classes $\mathcal {PT}$ and $\mathcal {PST}$ denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.
Algorithms for permutability in finite groups
2013
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
On generalised FC-groups in which normality is a transitive relation
2016
We extend to soluble FC∗ -groups, the class of generalised FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes , Serdica Math. J. 28(3) (2002), 241 254], the characterisation of finite soluble T-groups obtained recently in [G. Kaplan, On T-groups, supersolvable groups and maximal subgroups , Arch. Math. 96 (2011), 19 25].
Some local properties defining $T_0$-groups and related classes of groups
2016
[EN] We call G a Hall_X -group if there exists a normal nilpotent subgroup N of G for which G/N' is an X -group. We call G a T0 -group provided G/\Phi(G) is a T -group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define Hall_X -groups and T_0 -groups where X ∈ {T , PT , PST }; the classes PT and PST denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.