On minimal length factorizations of finite groups.
On simple distributively generated near-rings
On split pairs of rank 1
On the diameter of the intersection graph of a finite simple group
Let be a finite group. The intersection graph of is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of , and two distinct vertices and are adjacent if , where denotes the trivial subgroup of order . A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters of intersection...
On the intersection graph of a finite group
For a finite group , the intersection graph of which is denoted by is an undirected graph such that its vertices are all nontrivial proper subgroups of and two distinct vertices and are adjacent when . In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of .
On the lattice automorphisms of certain simple algebraic groups
On totally inert simple groups
A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.
On zero-symmetric nearrings with identity whose additive groups are simple
We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group as its additive group.
Partial Homogeneity in Locally Finite Groups.
Products of trees, lattices and simple groups.
Projective simplicity of groups of rational points of simply connected algebraic groups defined over number fields
Simple group contain minimal simple groups.
It is a consequence of the classification of finite simple groups that every non-abelian simple group contains a subgroup which is a minimal simple group.
Simple Groups and Möbius Planes of Even Order.
Simple groups with prescribed local structure
Simplicity of Neretin's group of spheromorphisms
Denote by , , the regular tree whose vertices have valence , its boundary. Yu. A. Neretin has proposed a group of transformations of , thought of as a combinatorial analogue of the diffeomorphism group of the circle. We show that is generated by two groups: the group of tree automorphisms, and a Higman-Thompson group . We prove the simplicity of and of a family of its subgroups.
Some groups whose reduced -algebra is simple
Sylow 2-subgroups of simple groups
The Lattice automorphisms of simple algebraic groups over F2.
Вложения конечных групп Шевалле и периодические линейные группы
Жордановы подгруппы простых алгебраических групп