We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one be...

for a finite group $g$‎, ‎we study the total character $tau_g$‎ ‎afforded by the direct sum of all the non-isomorphic irreducible‎ ‎complex representations of $g$‎. ‎we resolve for several classes of‎ ‎groups (the camina $p$-groups‎, ‎the generalized camina $p$-groups‎, ‎the groups which admit $(g,z(g))$ as a generalized camina pair)‎, ‎the problem of existence of a‎ ‎polynomial $f(x) in mathbb...

We show that soluble groups G of type Bredon-FP∞ with respect to the family of all virtually cyclic subgroups of G are always virtually cyclic. In such a group centralizers of elements are of type FP∞. We show that this implies the group is polycyclic. Another important ingredient of the proof is that a polycyclic-by-finite group with finitely many conjugacy classes of maximal virtually cyclic ...

‎in this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎the first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎the second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....

We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a cyclic p-group is permutation projective.

In this paper we prove that a free product of conjugacy separable groups A and B, amalgamating a cyclic subgroup, is conjugacy separable if A and B are subgroup separable, cyclic conjugacy separable, 2-free, and residually p-finite, for all prime numbers p. The following result is an example of the applications we obtain as consequences of our main theorem. Let A and B each be a free product of...

Examples of Fitting classes generated by certain periodic infinite groups are presented in this paper. The groups in question are finite extensions of direct products of quasi-cyclic (Priifer) groups and are, in particular, Cernikov groups. The methods applied follow closely those used for constructing Fitting classes of finite groups, especially in the case of nilpotent length three. 1991 Math...