‎The largest class of hyperstructures is the one which satisfies the weak properties; these are called $H_{v}$-structures‎. ‎In this paper we introduce a special product of elements in $H_{v}$-group $H$ and define a new class of $H_{v}$-groups called strongly $H_{v}$-groups‎. ‎Then we show that in strongly $H_{v}$-groups $beta=beta^{ast}$‎. ‎Also we express $theta$-hyperoperation and investigat...

We define the notions of strong and strict recurrency for actions countable ordered groups on σ-finite non atomic measure spaces with quasi-invariant measures. show that is equivalent to existence weakly wandering sets positive measure. also certain p.m.p ergodic system not strictly recurrent, which shows are equivalent.

Motivated by examples in infinite group theory, we classify the finite groups whose subgroups can never be decomposed as direct products.

It has long been known that the integral homology of a non-trivial finite group must be non-zero in infinitely many dimensions [15]. Recent work on the Sullivan Conjecture in homotopy theory has made it possible to extend this result to non-acyclic locally finite groups. For more general groups with torsion it becomes more difficult to make such a strong statement. Nevertheless we show that whe...