Geodesic
RECOGNIZING THE ALTERNATING GROUPS FROM THEIR PROBABILISTIC ZETA FUNCTION
Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 595-599

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DOI

Let $G$ be a finite group; there exists a uniquely determined Dirichlet polynomial $P_G(s)$ such that if $t \in \mathbb N$, then $P_G(t)$ gives the probability of generating $G$ with $t$ randomly chosen elements. We show that if $P_G(s)=P_{\text{Alt}(n)}(s)$, then $G/\text{Frat}\, G\cong \text{Alt}(n).$
DOI : 10.1017/S0017089504002010
Mots-clés : 20P05, 20D06 
DAMIAN, E.; LUCCHINI, A. RECOGNIZING THE ALTERNATING GROUPS FROM THEIR PROBABILISTIC ZETA FUNCTION. Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 595-599. doi: 10.1017/S0017089504002010
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     author = {DAMIAN, E. and LUCCHINI, A.},
     title = {RECOGNIZING {THE} {ALTERNATING} {GROUPS} {FROM} {THEIR} {PROBABILISTIC} {ZETA} {FUNCTION}},
     journal = {Glasgow mathematical journal},
     pages = {595--599},
     year = {2004},
     volume = {46},
     number = {3},
     doi = {10.1017/S0017089504002010},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504002010/}
}
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