Kinematic structures of certain loops
Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 543-551
Bokhee Im
Chonnam National University
Abstract : In this paper, we call a loop $F$ $kinematic$ if for $a, b \in F \setminus \{0 \}$, the following two conditions are valid: (i) the centralizer $Z(a)$ of $a$ is a commutative group under the induced operation from the loop $F$, and (ii) $Z(a)=Z(b)$ or $Z(a) \cap Z(b)= \{0 \}$, where 0 is the identity of $F$. Some examples of kinematic loops are given.
Keywords : kinematic loop, centralizer, reflection group
MSC numbers : 20N05, 51A25
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