Some Problems on Dedekind-Type Groups

Pseudo-cohomology of general extensions

“…for all M and for all pairs S and T of transversals of H in G. Clearly, then M (S) ab ∼ = M (T ) ab for all pairs S and T of transversals of H in G. We note that if H is a subgroup of a finite simple group having no complement, then M (S) = {e} for all transversals S of H in G [12]. For a finite solvable group it is known ( [12] Several other problems arise out of the discussions of the paper.…”

“…For a finite solvable group it is known ( [12] Several other problems arise out of the discussions of the paper. We also need to develop some methods to compute pseudo-cohomology and pseudo-homology groups of some important types of extensions.…”

A Study of Groups through Transversals

“…In [6], Tarski monsters has been characterized with the help of transversals. In [5], Lal shows that if all subgroups of a finitely generated solvable group are stable (any right transversals of a subgroup have isomorphic group torsion), then the group is nilpotent. In [2], it has been shown that if the isomorphism classes of transversals of a subgroup in a finite group is 3, then the subgroup itself has index 3.…”

A Note On Transversals

“…In [5], Tarski monsters has been characterized with the help of transversals. In [4], Lal shows that if all subgroups of a finitely generated solvable group are stable (any right transversals of a subgroup have isomorphic group torsion), then the group is nilpotent. In [2], it has been shown that if the isomorphism classes of transversals of a subgroup in a finite group is 3, then the subgroup itself has index 3.…”