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
Barzegar, R., Erfanian, A., & Farrokhi D. G., M. "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.
CHICAGO
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,
VANCOUVER
Barzegar R., Erfanian A., Farrokhi D. G. M. Finite groups with three relative commutativity degrees. BIMS. 2013;39(2):271-280.
