Abstract
AbstractSteiner loops of affine type are associated to arbitrary Steiner triple systems. They behave to elementary abelian 3-groups as arbitrary Steiner Triple Systems behave to affine geometries over $${\mathrm {GF}}(3)$$
GF
(
3
)
. We investigate algebraic and geometric properties of these loops often in connection to configurations. Steiner loops of affine type, as extensions of normal subloops by factor loops, are studied. We prove that the multiplication group of every Steiner loop of affine type with n elements is contained in the alternating group $$A_n$$
A
n
and we give conditions for those loops having $$A_n$$
A
n
as their multiplication groups (and hence for the loops being simple).
Funder
Università di Palermo
European Union
National Research, Development and Innovation Office
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
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