A Survey of NP-polyagroups survey article
Janez Ušan · Mathematica Moravica · 2006
This text is as an attempt to systemize the results about N P -polyagroups. Notion and example1.1.Definition [12]: Let k > 1, s ≥ 1, n = k • s + 1 and let (Q; A) be an n-groupoid.Then: we say that (Q; A) is an N P -polyagroup of the type (s, n -1) iff the following statements hold:2 • For all i ∈ {t • s + 1|t ∈ {0, 1, . . ., k}} and for every a n 1 ∈ Q there is exactly one x i ∈ Q such that the equalityRemark: For s = 1 (Q; A) is a (k + 1)-group, where k + 1 ≥ 3; k > 1.1.2.Example: Let (Q; •) be a group and let α be a mapping of the set Q into the set Q. Also, letfor all x 5 1 ∈ Q.Then (Q; A) is an N P -polyagroup of the type (2,4).Remark: Consult Prop.2.3 and Prop.2.1. Auxiliary proposition Proposition[12]: Let k > 1, s > 1, n = k • s + 1 and let (Q; A) be an n-groupoid.Also, let the following statements hold: 2000 Mathematics Subject Classification.Primary: 20N15.Key words and phrases.n-