On Mazurov triples of the sporadic group $B$ and Hamiltonian cycles of the Cayley graph

A system of generators of a group consisting of three involutions, two of which commute, is called a Mazurov triple. We describe algorithms for finding in an explicit form the Mazurov triples of one of the sporadic Monsters, the finite simple group $B$, and for constructing a Hamiltonian cycle in the Cayley graph of the finite group with Mazurov triple. We give examples of Hamiltonian cycles in the Cayley graphs of some groups.