Abstract: 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.
Keywords: left conjugacy closed loop; power associativity; left Cheban loop; autotopism; loop identities
DOI: DOI 10.14712/1213-7243.2026.004
AMS Subject Classification: 20N02 20N05