# A New Characterization of the Alternating Groups A5 and A6

### From NZJM

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**New Zealand Journal of Mathematics**

**Vol.** 42, (2012), **Pages** 149-155

**Alireza Khalili Asboei **

Department of Mathematics,

Shariati Sari Mazandaran,

Iran

**Abstract** Let *G* be a finite centerless group, let π(*G*) be the set of primes *p*
such that *G* contains an element of order *p* and let *n*_{p}(*G*) be the
number of Sylow *p* − subgroup of *G*, that is, *n*_{p}(*G*) = | *S**y**l*_{p}(*G*) | .
Set . If *N**S*(*G*) = *N**S*(*M*), where *M*
denotes one of the alternating simple groups *A*_{5} or *A*_{6}, then .

**Keywords** Finite group, Sylow subgroup.

**Classification** (MSC2000) 20D06, 20D20.

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