We study the computational complexity of the isomorphism and equivalence problems on systems of equations over a fixed finite group. We show that the equivalence problem is in P if the group is Abelian, and coNP-complete if the group is non-Abelian. We prove that if the group is non-Abelian, then the problem of deciding whether two systems of equations over the group are isomorphic is coNP-hard...

SO(3) it is the proper symmetry group of the icosahedron (and the dodecahedron). It is the unique finite subgroup of SO(3) which equals its own commutator subgroup—in fact, it is the unique non-abelian simple finite subgroup of SO(3). It can be thought of as the beginning or smallest member of the family of non-abelian finite simple groups. From the point of view of the McKay correspondence it ...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...