Abstract
Using coset diagrams it is shown that for every sufficiently large positive integer n, both the alternating group A n and the symmetric group S n are quotients of the group G 3,7, 168 = 〈A, B, C ¦ A 3 = B 7 = C 168 = (AB) 2 = (BC) 2 = (CA) 2 = (ABC) 2 = 1〉 , and hence that all but finitely many of the alternating groups A n can be generated by elements x and y satisfying the relations x 2 = y 3 = ( xy) 7 = ( x −1 y −1 xy) m = 1, where m = 84. This is the smallest known value of m for which this phenomenon occurs.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have