2 problems

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Non-subloop conjecture for Moufang elements in PACC-loops
Non-subloop conjecture. There exists a PACC-loop $Q$ in which $M(Q)$ is not a subloop.
Conjectureopenconjugacy-closed-loops loop-theoryarXiv posted 2 days ago
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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
Conjectureopenconjugacy-closed-loops finite-groups loopsarXiv posted 2 days ago

Non-subloop conjecture for Moufang elements in PACC-loops