Abstract
Let $G$ be a group. For an element $ain G$, denote by $cs(a)$ the second centralizer of~$a$ in~$G$, which is the set of all elements $bin G$ such that $bx=xb$ for every $xin G$ that commutes with $a$. Let $M$ be any maximal abelian subgroup of $G$. Then $cs(a)subseteq M$ for every $ain M$. The emph{abelian rank} (emph{$a$-rank}) of $M$ is the minimum cardinality of a set $Asubseteq M$ such that $bigcup_{ain A}cs(a)$ generates $M$. Denote by $S_n$ the symmetric group of permutations on the set $X={1,ldots,n}$. The aim of this paper is to determine the maximal abelian subgroups of $gx$ of $cor$~$1$ and describe a class of maximal abelian subgroups of $gx$ of $cor$ at most~$2$.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
