Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences

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Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences 7
1974-03-10 発行

対称空間の代数的モデルとしての準群(II)

On some Quasigroups of Algebraic Models of Symmetric Spaces(II)
Kikkawa, Michihiko
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In the previous paper [3], we introduced a concept of symmetric loop and showed that it is obtained, interchangeably, from a quasigroup of reflection with a base point. The latter is an algebraic model of symmetric space([4],[5]). In this paper, we shall investigate further properties of symmetric loop G about di-associaticity(§1)and show that the left inner mapping group is a subgroup of AutG(§2). In §3, we shall give an embedding of G into a group AutG*, the automorphism group of the quasigroup of reflection of G. The method of embedding was suggested, essentially, by Professor Kiyosi Yamaguti in his recent letter to the author.