Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups

Details Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups

2007-01-24

arxiv.org/abs/math/0701716v1

Abh. Math. Sem. Univ. Hamburg 75 (2006), 121-136

Mathematics

Group Theory

15 pages

Scientific paper

The variety of quasigroups satisfying the identity $(xy)(zy)=xz$ mirrors the variety of groups, and offers a new look at groups and their multiplication tables. Such quasigroups are constructed from a group using right division instead of multiplication. Their multiplication tables consist of circulant blocks which have additional symmetries and have a concise presentation. These tables are a reincarnation of the group matrices which Frobenius used to give the first account of group representation theory. Our results imply that every group matrix may be written as a block circulant matrix and that this result leads to partial diagonalization of group matrices, which are present in modern applied mathematics. We also discuss right division in loops with the antiautomorphic inverse property.

Affiliated with

Also associated with

No associations

Rating

Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-603970