Symmetric representation of the elements of finite groups
نویسنده
چکیده
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically represented elements in terms of their permutation representation. In particular, we represent elements of the group U3(3) : 2, where U3(3) is the projective special unitary group of 3× 3 matrices with entries in the field F3, as a permutation on fourteen letters from the projective general linear group PGL2(7), followed by a word of length at most two in the fourteen involutory symmetric generators.
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