Let G be a group and let Autc(G) be the group of central automorphisms of G. We say that a subgroup H of a group G is c-characteristic if α(H) = H for all α ∈ Autc(G). We say that a group G is c-characteristically simple group if it has no non-trivial c-characteristic subgroup. If every subgroup of G is c-characteristic then G is called co-Dedekindian group. In this paper we characterize c-char...

It is well known there is no finitely generated abelian group which has the R∞ property. We will show that also many non-finitely generated abelian groups do not have the R∞ property, but this does not hold for all of them! In fact we construct an uncountable number of infinite countable abelian groups which do have the R∞ property. We also construct an abelian group such that the cardinality o...

In this article we construct free groups and subgroups of finite index in the unit group of the integral group ring of a finite non-abelian group G for which every non-linear irreducible complex representation is of degree 2 and with commutator subgroup G′ a central elementary abelian 2-group.

a group $g$ is called metahamiltonian if all its non-abelian subgroups are normal‎. ‎the aim of this paper is to provide an updated survey of research concerning certain classes of generalized metahamiltonian groups‎, ‎in various contexts‎, ‎and to prove some new results‎. ‎some open problems are listed‎.

For a finite group $G$ we investigate the smallest positive integer $e(G)$ such that map sending $g\in G$ to $e(G)|G:C_G(g)|$ is generalized character of $G$. It turns out strongly influenced by local data, but behaves irregularly for non-abelian simple groups. We interpret as an elementary divisor certain non-negative integral matrix related table Our methods applied Brauer characters also ans...

Abstract We study word maps with constants on symmetric groups. Even though there are non‐trivial mixed identities of bounded length that valid for all groups, we show no such can hold in the limit a metric sense. Moreover, prove and content, short enough, have an image positive diameter, measured normalized Hamming metric, which is from below terms length. Finally, also every self‐map finite n...