%0 Journal Article %T Groups in which every non-abelian subgroup is self-centralizing %A Costantino Delizia %A Heiko Dietrich %A Primoz Moravec %A Chiara Nicotera %J Mathematics %D 2015 %I arXiv %X We study groups having the property that every non-abelian subgroup contains its centralizer. We describe various classes of infinite groups in this class, and address a problem of Berkovich regarding the classification of finite $p$-groups with the above property. %U http://arxiv.org/abs/1510.06545v1