Zorn's matrices and finite index subloops

Details Zorn's matrices and finite index subloops Zorn's matrices and finite index subloops

2002-04-22

arxiv.org/abs/math/0204270v1

Mathematics

Group Theory

15 pages

Scientific paper

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.

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