The classification of normalizing groups

João Araújo, Peter Jephson Cameron, James David Mitchell, Max Neunhoeffer

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Let $X$ be a finite set such that $|X|=n$. Let $\trans$ and $\sym$ denote respectively the transformation monoid and the symmetric group on $n$ points. Given $a\in \trans\setminus \sym$, we say that a group $G\leq \sym$ is $a$-normalizing if $$ \setminus G= .$$ If $G$ is $a$-normalizing for all $a\in \trans\setminus \sym$, then we say that $G$ is normalizing. The goal of this paper is to classify normalizing groups and hence answer a question posed elsewhere. The paper ends with a number of problems for experts in groups, semigroups and matrix theory.
Original languageEnglish
Pages (from-to)481–490
JournalJournal of Algebra
Publication statusPublished - Jan 2013


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