Groups with finite automorphism classes of subgroups
Groups with finite classes of conjugate subgroups.
Groups with finite conjugacy classes of subnormal subgroups
Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank
It is proved that if a locally soluble group of infinite rank has only finitely many non-trivial conjugacy classes of subgroups of infinite rank, then all its subgroups are normal.
Groups with Homological Duality Generalizing Poincaré Duality.
Groups with many nearly normal subgroups
Un sottogruppo di un gruppo si dice nearly normal se ha indice finito nella sua chiusura normale . In questa nota si caratterizzano i gruppi in cui ogni sottogruppo che non sia nearly normal soddisfa una fissata condizione finitaria per diverse scelte naturali della proprietà .
Groups with many nilpotent subgroups
Groups with metamodular subgroup lattice
A group G is called metamodular if for each subgroup H of G either the subgroup lattice 𝔏(H) is modular or H is a modular element of the lattice 𝔏(G). Metamodular groups appear as the natural lattice analogues of groups in which every non-abelian subgroup is normal; these latter groups have been studied by Romalis and Sesekin, and here their results are extended to metamodular groups.
Groups with minimal conditions related to finiteness properties on conjugacy classes
Groups with nearly modular subgroup lattice
A subgroup H of a group G is nearly normal if it has finite index in its normal closure . A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this article we...
Groups with Normalizer Condition.
Groups with One More Generator than Relators.
Groups with One More Generator than Relators.
Groups with only two nonlinear non-faithful irreducible characters
We determine the groups with exactly two nonlinear non-faithful irreducible characters whose kernels intersect trivially.
Groups with Restricted Conjugacy Classes
Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it is shown that...
Groups with Restricted Non-Normal Subgroups.
Groups with root-system of type .
Groups with small deviation for non-subnormal subgroups
We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent,...
Groups with soluble factor groups and projectivities
Groups with subnormal subgroups of bounded defect