Given generators for a group of permutations, it is shown that generators for the subgroups in a composition series can be found in polynomial time. The procedure also yields permutation representations of the composition factors. 1) Research supported by National Science Foundation Grants DCR-8403745 and DCR-8609491

Let G be a finite group and let T (G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We investigate the torsion-free part TF (G) of the group T (G) and look for generators of TF (G). We describe three methods for obtaining generators. Each of them only gives partial answers to the question but we obtain more p...

By the density of a finite graph we mean its average vertex degree. For an [Formula: see text]-generated group, Cayley in given set generators, is supremum densities taken over all subgraphs. It known that group with text] generators amenable if and only corresponding equals text]. A famous problem on amenability R. Thompson’s still open. Due to result Belk Brown, it standard text], at least Th...