6533b7d4fe1ef96bd1262d58

RESEARCH PRODUCT

Steiner Loops of Affine Type

Giovanni FalconeÁGota FigulaCarolin Hannusch

subject

Steiner triple systems steiner loops of affine type multiplication groups of loops finite geometries commutative Moufang loop.Settore MAT/03 - Geometria

description

Steiner 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 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 An and we give conditions for those loops having An as their multiplication groups (and hence for the loops being simple).

yearjournalcountryeditionlanguage
2020-01-01
10.1007/s00025-020-01273-6http://hdl.handle.net/10447/438455