For a finite group $G$ and a subgroup $H$ of $G$, the relative commutativity degree of $H$ in $G$, denoted by $d(H,G)$, is the probability that an element of $H$ commutes with an element of $G$. Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$. It is shown that a finite group $G$ admits three relative commutativity degrees if and only if $G/Z(G)$ is a non-cyclic group of order $pq$, where $p$ and $q$ are primes. Moreover, we determine all the relative commutativity degrees of some known groups.
Barzegar, R., Erfanian, A., & Farrokhi D. G., M. (2013). Finite groups with three relative commutativity degrees. Bulletin of the Iranian Mathematical Society, 39(2), 271-280.
MLA
R. Barzegar; A. Erfanian; M. Farrokhi D. G.. "Finite groups with three relative commutativity degrees". Bulletin of the Iranian Mathematical Society, 39, 2, 2013, 271-280.
HARVARD
Barzegar, R., Erfanian, A., Farrokhi D. G., M. (2013). 'Finite groups with three relative commutativity degrees', Bulletin of the Iranian Mathematical Society, 39(2), pp. 271-280.
VANCOUVER
Barzegar, R., Erfanian, A., Farrokhi D. G., M. Finite groups with three relative commutativity degrees. Bulletin of the Iranian Mathematical Society, 2013; 39(2): 271-280.
)