Article
| Title: | On loops that satisfy $x\cdot (x\cdot yx)z=(x\cdot xy)\cdot xz $ (English) |
| Author: | Jaiyéọlá, Tèmítọ́pẹ́ G. |
| Author: | George, Olufemi O. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 66 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 29-36 |
| Summary lang: | English |
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| Category: | math |
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| 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. (English) |
| Keyword: | left conjugacy closed loop |
| Keyword: | power associativity |
| Keyword: | left Cheban loop |
| Keyword: | autotopism |
| Keyword: | loop identities |
| MSC: | 20N02 |
| MSC: | 20N05 |
| DOI: | 10.14712/1213-7243.2026.004 |
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| Date available: | 2026-05-15T05:53:47Z |
| Last updated: | 2026-05-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153608 |
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