On a four-generator Coxeter group.
On a free action of a group on an Abelian group.
On a group acting locally freely on an Abelian group.
On a group that acts freely on an Abelian group.
On a New Characterization of Demuskin Groups.
On a Problem of Boone.
On a question of Deaconescu about automorphisms. - III
On a question of M. Conder
We show that the special linear group , over the integers, is not -generated. This gives a negative answer to a question of M. Conder.
On a result of G. Baumslag
On a subgroup of the affine Weyl group .
On almost finitely generated nilpotent groups.
On an algorithm to decide whether a free group is a free factor of another
We revisit the problem of deciding whether a finitely generated subgroup is a free factor of a given free group . Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of and exponential in the rank of . We show that the latter dependency can be made exponential in the rank difference rank - rank, which often makes a significant change.
On an algorithm to decide whether a free group is a free factor of another
We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.
On aspherical presentations of groups.
On asymptotic dimension of groups.
On centrally nilpotent loops
Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.
On embedding properties of -groups.
On explicit relations between cyclotomic numbers
On exponential growth rates for free groups.
Let Fp be a free group of rank p ≥ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of Fp is 2p-1. We show that the exponential growth rate τ of a group G with respect to a p-element generating set X is 2p-1 if and only if G is free on X; otherwise τ < 2p-1. We also prove that, for any finite generating set X of Fp which is disjoint from X-1, the exponential growth rate τ of Fp with respect to X is 2p-1 if and only if X is...
On finite 3-generated 2-groups of Alperin.