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RECOGNIZING THE ALTERNATING GROUPS FROM THEIR PROBABILISTIC ZETA FUNCTION

Published online by Cambridge University Press:  11 October 2004

E. DAMIAN  and
A. LUCCHINI
E. DAMIAN
Affiliation:
Dipartimento di Matematica, Università di Brescia, Via Valotti, 25133 Brescia, Italy e-mail: damian@ing.unibs.it, lucchini@ing.unibs.it
A. LUCCHINI
Affiliation:
Dipartimento di Matematica, Università di Brescia, Via Valotti, 25133 Brescia, Italy e-mail: damian@ing.unibs.it, lucchini@ing.unibs.it
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Abstract

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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 $G/\text{Frat}\, G\cong \text{Alt}(n).$

Keywords

20P0520D06
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 3 , September 2004 , pp. 595 - 599
Copyright
© 2004 Glasgow Mathematical Journal Trust