Let [Formula: see text] be a class of finite groups closed under taking subgroups, homomorphic images and extensions. It is known that if normal subgroup group then the image an text]-maximal in not, general, text]. We say reduction text]-theorem holds for if, every extension (i.e. contains as subgroup), number conjugacy classes subgroups same. The implies In this paper, we prove only all are c...

There are strong analogies between groups definable in o-minimal structures and real Lie groups. Nevertheless, unlike the real case, not every definable group has maximal definably compact subgroups. We study definable groups G which are not definably compact showing that they have a unique maximal normal definable torsion-free subgroup N ; the quotient G/N always has maximal definably compact ...

We call a group $G$ belongs to the class of groups $S_{p}'$, if for every $pd$-chief factor $A/B$ $G$, $((A/B)_{p})'=1$. In this paper, we investigate influence some second maximal subgroups which are related non-$c_{p}$-normal on structure $S_{p}'$.

Abstract We consider a generalisation of the Basilica group to all odd primes: p -Basilica groups acting on -adic tree. show that have -congruence subgroup property but not congruence nor weak property. This provides first examples weakly branch with such properties. In addition, give branch, which are super strongly fractal. compute orders quotients these groups, enable us determine Hausdorff ...

The purpose of this paper is to present a method for translating the problem of finding all maximal subgroups of finite groups into questions concerning groups that are nearly simple. (A finite group is called nearly simple if it has only one minimal normal subgroup and that it nonabelian and simple.) In view of the recently announced classification of all finite simple groups this seems to be ...

abstract. in this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.