Simulated factorizations II.
Small maximal sum-free sets.
Small-sum pairs in abelian groups
Let be an abelian group and two subsets of equal size such that and both have size . Answering a question of Bihani and Jin, we prove that if is aperiodic or if there exist elements and such that has a unique expression as an element of and has a unique expression as an element of , then is a translate of . We also give an explicit description of the various counterexamples which arise when neither condition holds.
Solvable subgroups of p-solvable semilinear groups.
Some additive applications of the isoperimetric approach
Let be a group and let be a finite subset. The isoperimetric method investigates the objective function , defined on the subsets with and , where is the product of by .In this paper we present all the basic facts about the isoperimetric method. We improve some of our previous results and obtain generalizations and short proofs for several known results. We also give some new applications.Some of the results obtained here will be used in coming papers to improve Kempermann structure...
Some problems in number theory that arise from group theory.
In this expository paper, we present several open problerns in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Some problems on splittings of groups.
Some questions on the number of generators of a finite group
Some Remarks on a Certain Class of Finite p-Groups.
Some results on the partitions of groups
Some results on the recognizability of the linear groups over the binary field
In this paper, we first find the set of orders of all elements in some special linear groups over the binary field. Then, we will prove the characterizability of the special linear group using only the set of its element orders.
Some simple groups which are determined by the set of their character degrees. II
Some supersolvability criteria for finite groups.
Splitting groups of prime order.
Splittings of Abelian groups by integers.
Splittings of Abelian groups by integers. (Short Communication).
Splittings of infinite abelian group.
Splittings of infinite abelian group. (Short Communication).
Still another proof of the existence of Sylow--subgroups.
Structure and derived length of finite p-groups possessing an automorphism of p-power order having exactly p fixpoints.