Related papers: On conjugate separability of nilpotent subgroups

We study the class of groups having the property that every non-nilpotent subgroup is equal to its normalizer. These groups are either soluble or perfect. We completely describe the structure of soluble groups and finite perfect groups with…

A group is $G$ commutative transitive or CT if commuting is transitive on nontrivial elements. A group $G$ is CSA or conjugately separated abelian if maximal abelian subgroups are malnormal. These concepts have played a prominent role in…

A group is CSA, if all of its maximal abelian subgroups are malnormal. It is known that every non-abelian CSA group is an equational domain. We generalize this result in two directions: we show that for a non-nilpotent group $G$ and a fixed…

Some properties of abnormal subgroups in generalized soluble groups will be considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it will be proven that a subgroup H of a radical group G is…

We provide sufficient conditions for a free amalgamated product of torsionfree nilpotent groups to be residually nilpotent. We also characterise the residual nilpotence of certain higher-dimensional amalgams of unipotent groups over the…

In this paper we study conjugacy and subgroup separability properties in the class of nilpotent $\mathbb{Q}[x]$-powered groups. Many of the techniques used to study these properties in the context of ordinary nilpotent groups carry over…

The structure of a group which is not nilpotent but all of whose proper subgroups are nilpotent has interested the researches of several authors both in the finite case and in the infinite case. The present paper generalizes some classic…

The present article studies nilpotent and Hamiltonian cancellative residuated lattices and their relationship with nilpotent and Hamiltonian lattice-ordered groups. In particular, results about lattice-ordered groups are extended to the…

Let $\mathfrak{Nil}$ be the class of nilpotent groups and $G$ be a group. We call $G$ a meta-$\mathfrak{Nil}$-Hamiltonian group if any of its non-$\mathfrak{Nil}$ subgroups is normal. Also, we call $G$ a para-$\mathfrak{Nil}$-Hamiltonian…

In this paper, we establish the theory of nilpotent hypergroups and study some properties of nilpotent hypergroups and provided some structural characterizations of nilpotent hypergroups.

Let $\pi$ be a set of primes. We show that $\pi$-separable groups have a conjugacy class of subgroups which specialize to Carter subgroups, i.e. self-normalizing nilpotent subgroups, or equivalently, nilpotent projectors, when specializing…

In this paper subcentral (resp., central) idempotent series and composition subcentral (resp., central) idempotent series in an inverse semigroup are introduced and investigated. It is shown that if $S=EG$ is a factorizable inverse monoids…

We develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse…

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms. We provide a complete classification of a finite group $G$ in which every maximal $A$-invariant subgroup containing the normalizer of some $A$-invariant…

Let $\mathfrak{Nil}$ be the class of nilpotent groups. This article explores the finiteness of meta and para-$\mathfrak{Nil}$-Hamiltonian groups or their derived subgroups when these groups contain a soluble subgroup of finite index or a…

Around 1980 commutator theory was generalized from groups to arbitrary algebras using the socalled term condition commutator. The semigroups that are abelian with respect to this commutator were classified by Warne (1994). We study what…

We construct examples of groups which have the same set of conjugacy class sizes as nilpotent groups, while their center is trivial. This answers a question posed by A. R. Camina in 2006.

Let $G$ be a finite soluble group and $G^{(k)}$ the $k$th term of the derived series of $G$. We prove that $G^{(k)}$ is nilpotent if and only if $|ab|=|a||b|$ for any $\delta_k$-values $a,b\in G$ of coprime orders. In the course of the…

Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…

In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shlyk's theorem.