Group invariants of certain Burn loop classes

Abstract

In this paper, we determine the collineation groups generated by the Bol reflections, the core, the automorphism groups and the full direction preserving collineation groups of the loops $B_{4n}$ and $C_{4n}$ given by R.P. Burn. We also prove some lemmas and use new methods in order to simplify the calculations in these groups.

Appeared in Bull. Belg. Math. Soc., 5:403-415, 1998