Zorn's matrices and finite index subloops
Group Theory
2007-05-23 v1 Rings and Algebras
Abstract
The Zorn's Algebra ZZ(R) has a multiplicative function called determinant with properties similar to the usual one. The set of elements in ZZ(R) with determinant 1 is a Moufang loop that we will denote by \GA. In our main result we prove that if R is a Dedekind algebraic number domain that contains an infinite order unit, each finite index subloop L, such that \GA has the weak Lagrange property relative to L, is congruence subloop. In addition, if R=\Z, then we present normal subloops of finite index in \GA that are not congruence subloops.
Cite
@article{arxiv.math/0204270,
title = {Zorn's matrices and finite index subloops},
author = {Fabio Enrique Brochero and Carmen Rosa Giraldo},
journal= {arXiv preprint arXiv:math/0204270},
year = {2007}
}
Comments
15 pages