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Keywords:
left conjugacy closed loop; power associativity; left Cheban loop; autotopism; loop identities
left conjugacy closed loop; power associativity; left Cheban loop; autotopism; loop identities
Summary:
An LTWC is a loop that satisfies $x\cdot (x\cdot yx)z=(x\cdot xy)\cdot xz$. LTWC loops are proved to be power associative and left conjugacy closed (LCC). An LCC loop is LTWC if and only if $ x(x\cdot yx)=(x\cdot xy)x$. Connections to left Bol loops, left Cheban loops and loops satisfying $(xy\cdot x)\cdot xz=x\cdot(yx\cdot x)z$ (LWPC) are also considered.
References:
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