Nilpotency in automorphic loops of prime power order

Details Nilpotency in automorphic loops of prime power order Nilpotency in automorphic loops of prime power order

2010-11-03

arxiv.org/abs/1011.0982v2

Mathematics

Group Theory

13 pages, amsart; v2: minor changes suggested by referee; to appear in J. Algebra

Scientific paper

A loop is automorphic if its inner mappings are automorphisms. Using so-called associated operations, we show that every commutative automorphic loop of odd prime power order is centrally nilpotent. Starting with anisotropic planes in the vector space of $2\times 2$ matrices over the field of prime order $p$, we construct a family of automorphic loops of order $p^3$ with trivial center.

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