On finite groups with a given number of exterior centralizers

Abstract

A group G is called n-centralizer if it has n distinct centralizers. In this paper, in analogs to n-centralizer, we say a group G is n-exterior centralizer provided G has n distinct exterior centralizers. The current paper is devoted to characterize all groups that are n-exterior centralizer, where $n\in \{1,2,3,4,5\}$.

Keywords:

• Centralizer
• exterior centralizer
• non-Abelian exterior products
• Schur multiplier

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D99
• 20F99
• 20E99