Li, Xianhua Li, Shiheng
Published in
Siberian Mathematical Journal

We introduce the notion of θ-pair of a proper subgroup of a finite group and give necessary and sufficient conditions for supersolvability and nilpotence of a finite group. As application, we give a proof to a recent open problem of Skiba in the unsolved problems in group theory.

Pittet, Ch. Saloff-Coste, L.
Published in
Journal of the European Mathematical Society

We establish the lower bound p2t(e,e)≿exp(-t1/3), for the large times asymptotic behaviours of the probabilities p2t(e,e) of return to the origin at even times 2t, for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r, such that any of its...

Deryabina, G. S. Krasil'nikov, A. N.
Published in
Siberian Mathematical Journal

Given an arbitrary identity v=1, there exists a positive integer N=N(v) such that for every metabelian group G and every generating set A for G the following holds: If each subgroup of G generated by at most N elements of A satisfies the identity v=1 then the group G itself satisfies this identity. A similar assertion fails for center-by-metabelian...

Liu, Weijun Li, Huiling
Published in
Science in China Series A: Mathematics

Let S be a finite linear space, and letG be a group of automorphisms of S. IfG is soluble and line-transitive, then for a givenk but a finite number of pairs of (S, G),S hasv= pn points andG ⩽AΓL(1,pn).

Pálfy, Péter Pál
Published in
Periodica Mathematica Hungarica

For any finite solvable group G we show that if three primes dividing the degrees of certain irreducible characters of G are given, then there exists an irreducible character of G with degree divisible by at least two of the given primes.

Ebanks, Bruce Stetkær, Henrik
Published in
Aequationes mathematicae

We provide an elementary way to compute continuous solutions of the 2-cocycle functional equation on solvable locally compact groups. Examples are given for certain linear groups. By “elementary” we mean that nothing is used from differential geometry, theory of Lie groups, or group cohomology.