The free commutative automorphic $2$ -generated loop of nilpotency class $3$

preprint2015arXivOpen access

A loop is automorphic if all its inner mappings are automorphisms. We construct the free commutative automorphic $2$ -generated loop of nilpotency class $3$ . It has dimension $8$ over the integers.

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The free commutative automorphic $2$ -generated loop of nilpotency class $3$

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The free commutative automorphic 222-generated loop of nilpotency class 333

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The free commutative automorphic $2$ -generated loop of nilpotency class $3$