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Keywords:
dihedral group; Moufang loop; cyclic extension; semidirect product
dihedral group; Moufang loop; cyclic extension; semidirect product
Summary:
This paper completely solves the isomorphism problem for Moufang loops $Q = GC$ where $G\unlhd Q$ is a noncommutative group with cyclic subgroup of index two and $|Z(G)| \le 2$, $C$ is cyclic, $G\cap C = 1$, and $Q$ is finite of order coprime to three.
References:
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[2] Chein O.: Moufang loops of small order. Mem. Amer. Math. Soc. 13 (1978), no. 197. MR 0466391 | Zbl 0378.20053
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[4] Gagola S.M., III: Cyclic extensions of Moufang loops induced by semi-automorphisms. J. Algebra Appl. 13 (2014), no. 4, Article ID 1350128. DOI 10.1142/S0219498813501284 | MR 3153863 | Zbl 1296.20028
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