RECOGNITION OF ALTERNATING GROUPS OF DEGREES r + 1 AND r + 2 FOR PRIME r AND THE GROUP OF DEGREE 16 BY THEIR ELEMENT ORDER SETS

It is proved that finite group whose element order set is the same as that of an alternating group A(n) of degree n=r+1 or r+2 for prime r > 5 or n = 16 is isomorphich to A(n).