In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if R is generalised dihedral group and CI-group, then for every odd prime p Sylow p-subgroup has order p, or 9. Consequently, any CI-group with quotient same restriction, that

a subgroup $x$ of a group $g$ is almost normal if the index $|g:n_g(x)|$ is finite, while $x$ is nearly normal if it has finite index in the normal closure $x^g$. this paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...

Let X be a compact bordered Klein surface of algebraic genus p ≥ 2 and let G = Γ∗/Λ be a group of automorphisms of X where Γ∗ is a noneuclidian chrystalographic group and Λ is a bordered surface group. If the order of G is 4q (q−2) (p−1), for q ≥ 3 a prime number, then the signature of Γ∗ is (0;+; [−]; {(2, 2, 2, q)}). These groups of automorphisms are called generalizedM∗-groups. In this paper...