The p-groups satisfying the condition: each cyclic subgroup is contained in the center or has a trivial intersection with it

Pylyavska, OlhaShatohina, Ju.2015-12-222015-12-222006Pylyavska Olha, The p-groups satisfying the condition : each cyclic subgroup is contained in the center or has a trivial intersection with it / O. Pylyavska, Ju. Shatohina // Наукові записки НаУКМА. - 2006. - Т. 51 : Фізико-математичні науки. - С. 3-4.https://ekmair.ukma.edu.ua/handle/123456789/7597Y. Berkovich proposed the next problem: "Suppose that p-group G satisfies the following condition: if Z is a cyclic subgroup o f G then either Z ≤ Z(G) or Z ⋂ Z(G) = {1}. Classify all such groups". We have proved that abelian p-groups and p-groups with exponent p exhaust all regular p-groups satisfying this condition.enР-групитривіальний перетинЗ.ЯнкВ.Чепулічуциклічна підгрупаp-groupThe p-groups satisfying the condition: each cyclic subgroup is contained in the center or has a trivial intersection with itР-групи, що задовольняють умови: кожна циклічна підгрупа або міститься у центрі групи, або має з ним тривіальний перетинArticle