Geodesic
The Number of Isomorphism Classes of Finite Groups with Given Element Orders
Algebra i logika, Tome 41 (2002) no. 1, pp. 70-82.

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Let $G$ be a finite group and $\pi_e(G)$ the set of element orders of $G$. Denote by $h(\pi_e(G))$ the number of isomorphism classes of finite groups $H$ satisfying $\pi_e(H)=\pi_e(G)$. We prove that if $G$ has at least three prime graph components, then $h(\pi_e(G))\in\{1, \infty\}$.
Keywords: finite group, set of element orders of a group, prime graph. 
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H. Deng; M. S. Lucido; W. Shi. The Number of Isomorphism Classes of Finite Groups with Given Element Orders. Algebra i logika, Tome 41 (2002) no. 1, pp. 70-82. http://geodesic.mathdoc.fr/item/AL_2002_41_1_a3/

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