In this note an ‘extended Burnside ring’ is defined, generated by classes of semisimple module categories over Rep(G) with quasifibre functors. Here G is a finite group and representations are taken over an algebraically closed field of characteristic 0. It is shown that this is equivalent to a ring generated by centrally extended G-sets and hence the name. Ring homomorphisms into the multiplic...

INTRODUCTION. If X is a CW complex with cells only in even dimensions and R is a ring, then, by an elementary result in cellular cohomology theory, the ordinary eohomology H*(X;R) of X with R coefficients is a free, 7/-graded R-module. Since this result is quite useful in the study of well-behaved complex manifolds like projective spaces or Grassmannians, it would be nice to be able to generali...

We introduce a model for random groups in varieties of $n$-periodic as quotients triangular groups. show that an explicit $d_{\mathrm{crit}}\in(1/3,1/2)$, densities $d\in(1/3,d_{\mathrm{crit}})$ and $n$ large enough, the produces \emph{infinite} As application, we obtain, every fixed enough $n$, $p\in (1,\infty)$ infinite group with points all isometric actions on $L^p$-spaces. Our main contrib...

A group is called simple if it has more than one element and if its only normal subgroups are the trivial subgroup and the whole group. In other words, it is a group with precisely two normal subgroups. It is an elementary exercise to show that the abelian simple groups are precisely the finite cyclic groups of prime order. The nonabelian simple groups, on the other hand, are far more complicat...

In the character theory of finite groups the Burnside-Brauer Theorem is a wellknown result which deals with products of characters in finite groups. In this paper, we first define the character products for table algebras and then by observing the relationship between the characters of a table algebra and the characters of its quotient, we provide a condition in which the products of characters...

In this note, we present a notion of species isomorphism for fibered Burnside rings. We prove that can be restricted to an mark tables, it extended between the ghost rings and provide three additional characterizations concept.