190 research outputs found
Products of conjugacy classes in finite unitary groups and
For the finite groups GU(3), SU(3), GL(3), SL(3) over a finite field we solve
the class product problem, i.e., we give a complete list of -tuples of
conjugacy classes whose product does not contain the identity matrix
Basic nets in the projective plane
The notion of basic net (called also basic polyhedron) on plays a
central role in Conway's approach to enumeration of knots and links in .
Drobotukhina applied this approach for links in using basic nets on
. By a result of Nakamoto, all basic nets on can be obtained from a
very explicit family of minimal basic nets (the nets , ,
in Conway's notation) by two local transformations. We prove a similar result
for basic nets in .
We prove also that a graph on is uniquely determined by its pull-back
on (the proof is based on Lefschetz fix point theorem).Comment: 14 pages, 15 figure
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