3 problems

The four-cycle conjecture for the abelian loop
Four-cycle conjecture. There are infinitely many such quartets.
opencombinatorics loops number-theory
0 responses
09
The nonassociative loop-switch strategy conjecture
Let $\mathcal{L}=(\{1,a,b,c,d\},\ast)$ be the smallest loop that is not a group, with multiplication operation $\ast$ . Loop-switch strategy conjecture. There exists a nontrivial ad…
openloops nonassociative-algebra surjective-strategies
0 responses
04
The right inner mapping group conjecture for simple right conjugacy closed loops
The right inner mapping group conjecture. The right inner mapping group of $(Q,\circ_f)$ is exactly
openconjugacy-closed-loops finite-groups loops
0 responses
06

The four-cycle conjecture for the abelian loop