The theory of nonabelian cohomology is used to show that the set of fixed points of a finite group acting on a Siegel modular space is a union of Shimura varieties

A generalised tetrahedron group is the colimit of a triangle of groups whose vertex groups are generalised triangle groups and whose edge groups are finite cyclic. We prove an improved Spelling Theorem for generalised triangle groups which enables us to compute the precise Gersten-Stallings angles of this triangle of groups, and hence obtain a classification of generalised tetrahedron groups ac...

In this paper, we essentially finish the classification of those finite 2, 3-groups G having integral group rings with the multiplicative Jordan decomposition (MJD) property. If G is abelian or a Hamiltonian 2-group, then it is clear that Z[G] satisfies MJD. Thus, we need only consider the nonabelian case. Recall that the 2-groups with MJD were completely determined by Hales, Passi and Wilson, ...

We study model-theoretic and stability-theoretic properties of the nonabelian free group in the light of Sela’s recent result [15] on stability and results announced by Bestvina and Feighn on “negligible subsets” of free groups. We point out analogies between the free group and socalled bad groups of finite Morley rank, and prove “non CM -triviality”

This study examines the same-order type of G, suppose G be a finite group that α(G)=S_tt∈πe(G) and define nse(G) or α(G) is whose S_t number elements order t t∈π_e (G) π_e set G. If |G|=n in then we say α_n-group. Shin [1] showed every α_2-group nilpotent α_3-group solvable. In addition, structure such proved if an α_n-group |π(G)|≤n, conjectures researcher nonabelian simple group. proves group...

In this paper we show that several classes of elementary properties (properties definable by sentences of a first order logic) of groups hold for all nonabelian free groups. These results are obtained by examining special embeddings of these groups into one another which preserve the properties in question. I. It has long been conjectured that the finitely generated nonabelian free groups are e...

In this paper, first we introduce the notion of a nonabelian embedding tensor, which is generalization an tensor. Then Leibniz-Lie algebra, underlying algebraic structure and can also be viewed as Leibniz algebra. Next using derived bracket, construct differential graded Lie whose Maurer-Cartan elements are exactly tensors. Consequently, obtain algebra that governs deformations Finally, define ...

A group G is a CI-group with respect to graphs if two Cayley graphs of G are isomorphic if and only if they are isomorphic by a group automorphism of G. We show that an infinite family of groups which include Dn × F3p are not CI-groups with respect to graphs, where p is prime, n 6= 10 is relatively prime to 3p, Dn is the dihedral group of order n, and F3p is the nonabelian group of order 3p.