On the -conjecture
On the Nielsen Method in Free Products with Amalgamated Subgroups.
On the nilpotency of the Jacobson radical of semigroup rings.
On the nilpotent rank of partial transformation semigroups.
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