Normalizer Of Subloops

Abstract

In [1] Albert proved that the centre Z of a loop (G,.) is isomorphic to the centre Z_M of the multiplication group M(G) of G. In this paper, we prove that the normalizer N(H) of subloop H in G is in one-to-one correspondence with the normalizer N(M(H)) of the subgroup M(H) in M(G).

Keywords: Normalizer, Loop, Subgroup, Multiplication group