Following the literature, a group G is called a group of central type if G has an irreducible character that vanishes on $G\setminus Z(G)$. Motivated by this definition, we say that a character $\chi \in \mathrm{Irr}(G)$ has central type if χ vanishes on $G\setminus Z(\chi )$, where $Z(\chi )$ is the center of χ. Groups where every irreducible character has central type have been studied previously under the name GVZ-groups (and several other names) in the literature. In this paper, we study the groups G that possess a nontrivial, normal subgroup N such that every character of G either contains N in its kernel or has central type. The structure of these groups is surprisingly limited and has many aspects in common with both central type groups and GVZ-groups.

以下文献中，一组ģ被称为一组中心型如果ģ具有上消失的不可约字符$G\setminus ž（G）$。受此定义的激励，我们说一个字符$\chi \in \mathrm{Irr}（G）$如果χ消失，则具有中心类型$G\setminus ž（\chi ）$， 在哪里 $ž（\chi ）$是χ的中心。先前已经研究了每个不可简化字符都具有中心类型的组，在文献中以GVZ-groups（以及其他几个名称）的名称进行了研究。在本文中，我们研究具有非平凡，正常子组N的组G，以使G的每个字符在其内核中包含N或具有中心类型。这些基团的结构令人惊讶地受到限制，并且具有与中心型基团和GVZ基团相同的许多方面。