An improved method for generating the centralizer of an involution (Q1568655)

The author compares two methods of computation of the centralizer of an involution in a finite group: the first is due to R. Parker and \textit{S. Norton} [Santa Cruz Conf. 1979, Proc. Symp. Pure Math. 37, 271-277 (1980; Zbl 0448.20018)] and the second to the author. In particular, the author illustrates his method by proving the following result: The group \(\langle x,y\mid x^2=y^7=(xy)^{11}=[x,y]^2=[x,y^2]^3=[x,y^3]^3=1\rangle\) is isomorphic to \(2^2\cdot U_6(2)\).