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

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 ...

‎let $g$ be a finite group and let $n$ be a normal subgroup of $g$‎. ‎suppose that ${rm{irr}} (g | n)$ is the set of the irreducible characters of $g$ that contain $n$ in their kernels‎. ‎in this paper‎, ‎we classify solvable groups $g$ in which the set $mathcal{c} (g) = {{rm{irr}} (g | n) | 1 ne n trianglelefteq g }$ has at most three elements‎. ‎we also compute the set $mathcal{c}(g)$ for suc...

In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.