in this paper, we consider locally graded groups in which every non-permutable subgroup is soluble of bounded derived length.

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

a normal subgroup $n$ of a group $g$ is said to be an‎ ‎$emph{omissible}$ subgroup of $g$ if it has the following property‎: ‎whenever $xleq g$ is such that $g=xn$‎, ‎then $g=x$‎. ‎in this note we construct various groups $g$‎, ‎each of which has an omissible subgroup $nneq 1$ such that $g/ncong sl_2(k)$ where $k$ is a field of positive characteristic‎.

A group G has subnormal deviation at most 1 if, for every descending chain H0 > H1 > . . . of non-subnormal subgroups of G, for all but finitely many i there is no infinite descending chain of non-subnormal subgroups of G that contain Hi+1 and are contained in Hi. This property P, say, was investigated in a previous paper by the authors, where soluble groups with P and locally nilpotent groups ...