Geodesic
On a generalization of Fermat's little theorem
Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 199-201.

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We obtain a congruence type arithmetic relation on the set of all triples $(G,H,P)$, where $G$ is a finite group, $H$ is a subgroup, and $P$ is a representation of $G$ by permutations. This relation becomes Fermat's Little Theorem in the case when $G=Z_p$, $H=1$, and $P$ is the regular representation of $G$. 
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S. P. Strunkov. On a generalization of Fermat's little theorem. Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 199-201. http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a8/

[1] Strunkov S. P., “O kratnostyakh neprivodimykh komponent predstavlenii konechnykh grupp podstanovkami”, UMN, 40:1 (1985), 177–178 | MR | Zbl

[2] Kholl M., Kombinatorika, Mir, M., 1970 | MR