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Laterally commutative heaps and TST-spaces. (English) Zbl 0674.20045

(Q,( )) is called a laterally commutative heap if \((abc)=(cba)\), \(((abc)de)=(a(bcd)e)\), \((abb)=a\). Let S be a family of mappings of Q, then (Q,S) is said to be a TST-space if (i) for every \(\sigma\in S\) the mapping \(\sigma\) \(\circ \sigma\) is the identity, (ii) for any \(a,b\in Q\) there is \(\sigma\in S\) such that \(\sigma (a)=b\), (iii) from \(\sigma_ 1,\sigma_ 2,\sigma_ 3\in S\) it follows \(\sigma_ 3\circ \sigma_ 2\circ \sigma_ 1\in S\). Two known theorems imply the following Theorem: There is a laterally commutative heap (Q,( )) iff there is a TST-space (Q,S). The author gives a new direct proof of this Theorem.
Reviewer: E.Brozikova

MSC:

20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
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