Left gyrotransversal of a subgroup

Definition

Definition with symbols

Let $H$ be a subgroup of a group $G$. Then, a left transversal $B$ (viz a system of left coset representatives) of $H$ in $G$ is termed a left gyrotransversal if it satisfies all the following conditions:

• The identity element belongs to $B$ (and is thus the coset representative for $H$)
• $B=B^{-1}$. In other words, the inverse of any left coset representative is also a left coset representative
• $hBh^{-1}=B$ for any $h\in H$, or equivalently, $H\subseteq N_{G}(B)$