The Cayley graph of a subgroup of the Burnside group B<sub>0</sub>(2, 5)
Let B0(2, 5) = (a1, a2) be the largest two-generator Burnside group of exponent five. It has the order 534. We define an automorphism ^ under which every generator is mapped into another generator. Let CBo(2,5)(0(2, 5). It is known that |CBo(2,5)(^)| = 517. We have calculated the growth function of this group relative to the minimal generating set X. As a result, the diameter and the average diameter of CBo(2,5)(<^) are computed: (C) = 33, (C) ~ 26,1.