3-nets realizing a group in a projective plane

Details 3-nets realizing a group in a projective plane 3-nets realizing a group in a projective plane

2011-04-22

arxiv.org/abs/1104.4439v3

Mathematics

Algebraic Geometry

Scientific paper

In a projective plane PG(2,K) defined over an algebraically closed field K of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky, arises from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family. Urzua's 3-nets realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds true in characteristic p>0 apart from three possible exceptions Alt_4, Sym_4 and Alt_5.

Affiliated with

Also associated with

No associations

Rating

3-nets realizing a group in a projective plane 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 3-nets realizing a group in a projective plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and 3-nets realizing a group in a projective plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-330776