On the Nilpotent representations of GLn (O).
On the noncommuting graph associated with a finite group.
On the (non-)contractibility of the order complex of the coset poset of an alternating group
On the nontrivial solvability of systems of homogeneous linear equations over in ZFC
Motivated by the paper by H. Herrlich, E. Tachtsis (2017) we investigate in ZFC the following compactness question: for which uncountable cardinals , an arbitrary nonempty system of homogeneous -linear equations is nontrivially solvable in provided that each of its subsystems of cardinality less than is nontrivially solvable in ?
On the normalizer of a group in the Cayley representation.
On the number of Abelian groups of a given number.
On the number of abelian groups of a given order
On the number of abelian groups of a given order (supplement)
1. Introduction. The aim of this paper is to supply a still better result for the problem considered in [2]. Let A(x) denote the number of distinct abelian groups (up to isomorphism) of orders not exceeding x. We shall prove Theorem 1. For any ε > 0, , where C₁, C₂ and C₃ are constants given on page 261 of [2]. Note that 50/199=0.25125..., thus improving our previous exponent 40/159=0.25157... obtained in [2]. To prove Theorem 1, we shall proceed along the line of approach presented in [2]....
On the Number of Characters in Blocks of Finite General Linear, Unitary and Symmetric Groups.
On the number of conjugacy classes in a finite group
On the number of conjugacy classes of pi-elements in a finite group
On the number of facets of three-dimensional Dirichlet stereohedra. II: Non-cubic groups.
On the number of generating pairs for the groups and .
On the number of isomorphism classes of derived subgroups
We show that a finite nonabelian characteristically simple group satisfies if and only if , where is the number of isomorphism classes of derived subgroups of and is the set of prime divisors of the group . Also, we give a negative answer to a question raised in M. Zarrin (2014).
On the number of maximal theta pairs in a finite group
On the number of normal subgroups of a given prime index
On the number of permutations arising from a problem in cell-biology.
On the number of rim hook tableaux
On the number of solutions of equation in a finite group
Theorem A yields the condition under which the number of solutions of equation in a finite -group is divisible by (here is a fixed positive integer). Theorem B which is due to Avinoam Mann generalizes the counting part of the Sylow Theorem. We show in Theorems C and D that congruences for the number of cyclic subgroups of order which are true for abelian groups hold for more general finite groups (for example for groups with abelian Sylow -subgroups).
On the number of subgroups of finite abelian groups
Letwhere denotes the number of subgroups of all abelian groups whose order does not exceed and whose rank does not exceed , and is the error term. It is proved that