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In this paper we show that evolution algebras over any given field \Bbbk are universally finite. In other words, given any finite group G, there exist infinitely many regular evolution algebras X such that Aut(X)\cong G. The proof is built upon the construction of a covariant faithful functor from the category of finite simple (non oriented) graphs to the category of (finite dimensional) regular evolution algebras. Finally, we show that any constant finite algebraic affine group scheme \mathbf {G} over \Bbbk is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra. [ABSTRACT FROM AUTHOR]

We provide a nilpotency criterion for fusion systems in terms of the vanishing of its cohomology with twisted coefficients. [ABSTRACT FROM AUTHOR]

We prove that the isomorphism type of a large class of groups is determined by the class of differential graded algebras over an integral domain with mild conditions, on which these groups act faithfully. [ABSTRACT FROM PUBLISHER]

We prove that every finite group G can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces X. To construct those spaces we introduce a new technique which leads, for example, to the existence of infinitely many inflexible manifolds. Further applications to representation theory will appear in a separate paper. [ABSTRACT FROM AUTHOR]

We consider classifying spaces of a family of p-groups and prove that mod p cohomology enriched with Bockstein spectral sequences determines their homotopy type among p-completed CW-complexes. [ABSTRACT FROM AUTHOR]

Abstract: Often a localization functor (in the category of groups) sends a finite simple group to another finite simple group. We study when such a localization also induces a localization between the automorphism groups and between the universal central extensions. As a consequence we exhibit many examples of localizations of finite simple groups which are not simple. [Copyright &y& Elsevier]