Geodesic
On $M$-divisibility of stable laws of stable laws
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 559-562 
V. M. Zolotarev. On $M$-divisibility of stable laws of stable laws. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 559-562. http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a15/
@article{TVP_1967_12_3_a15,
     author = {V. M. Zolotarev},
     title = {On $M$-divisibility of stable laws of stable laws},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {559--562},
     year = {1967},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a15/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A one dimensional distribution $F$ is called $M$-infinitely divisible ($M$-i. d.) if there exists a sequence of integers $0 such that for every $n_j$ it equal to the distribution of the product of some $n_j$ independent identically distributed random variables. It is shown that the stable laws with parameters ($\alpha<1$, $\gamma=0$), ($\alpha=1$, $\beta=0$), ($\alpha>1$, $\gamma=0$, $\beta=0$) are $M$-i. d. but the stable laws with parameters ($\alpha>1$, $\gamma=0$, $\beta\ne0$) are not $M$-i. d.