Free products of finitary linear groups

Finitary Permutation Groups

A finitary permutation group is a natural generalization of a finite permutation group. The structure of a transitive finitary permutation group is surprisingly simple when its degree is infinite. Here we study primitivity, following P. M. Neumann’s work in the 1970s. We also study generalized solubility conditions on these groups. These notes arose from lectures aimed at an audience who had se...

Contraction-free proofs and finitary games for Linear Logic

In the standard sequent presentations of Girard’s Linear Logic [10] (LL), there are two ”non-decreasing” rules, where the premises are not smaller than the conclusion, namely the cut and the contraction rules. It is a universal concern to eliminate the cut rule. We show that, using an admissible modification of the tensor rule, contractions can be eliminated, and that cuts can be simultaneously...

Free Products of Absolute Galois Groups *

Profinite Topologies in Free Products of Groups

Let H be an abstract group and let C be a variety of finite groups (i.e., a class of finite groups closed under taking subgroups, quotients and finite direct products); for example the variety of all finite p-groups, for a fixed prime p. Consider the smallest topology on H such that all the homomorphism H −→ C from H to any group C ∈ C (endowed with the discrete topology) is continuous. We refe...

homogenous finitary symmetric groups

we characterize strictly diagonal type of embeddings offinitary symmetric groups in terms of cardinality and the characteristic. namely, we prove thefollowing.let $kappa$ be an infinite cardinal. if$g=underset{i=1}{stackrel{infty}bigcup} g_i,$ where $ g_i=fsym(kappa n_i)$,$(h=underset{i=1}{stackrel{infty}bigcup}h_i, $ where $ h_i=alt(kappa n_i) ), $ is a group of strictly diagonal type and$xi=(...