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Let $G$ be an abelian group and $A, B$ two subsets of equal size $k$ such that $A + B$ and $A + A$ both have size $2 k - 1$ . Answering a question of Bihani and Jin, we prove that if $A + B$ is aperiodic or if there exist elements $a \in A$ and $b \in B$ such that $a + b$ has a unique expression as an element of $A + B$ and $a + a$ has a unique expression as an element of $A + A$ , then $A$ is a translate of $B$ . We also give an explicit description of the various counterexamples which arise when neither condition holds.

Solvable subgroups of p-solvable semilinear groups.

Burkhard Külshammer (1990)

Journal für die reine und angewandte Mathematik

Some additive applications of the isoperimetric approach

Yahya O. Hamidoune (2008)

Annales de l’institut Fourier

Let $G$ be a group and let $X$ be a finite subset. The isoperimetric method investigates the objective function $| (X B) ∖ X |$ , defined on the subsets $X$ with $| X | \geq k$ and $| G ∖ (X B) | \geq k$ , where $X B$ is the product of $X$ by $B$ .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.

Alexander Moretó (2007)

Publicacions Matemàtiques

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.

Sándor Szabó (1986)

Aequationes mathematicae

Some questions on the number of generators of a finite group

Andrea Lucchini (1990)

Rendiconti del Seminario Matematico della Università di Padova

Some Remarks on a Certain Class of Finite p-Groups.

Ian Kiming (1995)

Mathematica Scandinavica

Some results on the partitions of groups

M. Farrokhi D. G. (2011)

Rendiconti del Seminario Matematico della Università di Padova

Some results on the recognizability of the linear groups over the binary field

Mohammad Reza Darafsheh, Yaghoub Farjami, M. Khademi, Ali Reza Moghaddamfar (2005)

Commentationes Mathematicae Universitatis Carolinae

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 $PSL (13, 2)$ using only the set of its element orders.

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Schur multipliers of p-groups.

Sequenceable groups and related topics.

Simulated factorizations II.

Small maximal sum-free sets.

Small-sum pairs in abelian groups

Solvable subgroups of p-solvable semilinear groups.

Some additive applications of the isoperimetric approach

Some problems in number theory that arise from group theory.

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

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).

Currently displaying 1 – 20 of 28