Elements Generating a Proper Normal Subgroup of the Cremona Group

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Generating the Infinite Symmetric Group Using a Closed Subgroup and the Least Number of Other Elements

Let S∞ denote the symmetric group on the natural numbers N. Then S∞ is a Polish group with the topology inherited from NN with the product topology and the discrete topology on N. Let d denote the least cardinality of a dominating family for NN and let c denote the continuum. Using theorems of Galvin, and Bergman and Shelah we prove that if G is any subgroup of S∞ that is closed in the above to...

On Marginal Automorphisms of a Group Fixing the Certain Subgroup

Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...

finite groups with a certain number of elements pairwise generating a non-nilpotent subgroup

Generating Random Elements of a Finite Group

We present a “practical” algorithm to construct random elements of a finite group. We analyse its theoretical behaviour and prove that asymptotically it produces uniformly distributed tuples of elements. We discuss tests to assess its effectiveness and use these to decide when its results are acceptable for some matrix groups.