On a reformulation of the commutator subgroup
| Autor: | Cummings, Paul A, Ortega, Brian |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For semigroup $S$, a commutative congruence $\sigma_{orient}$ on $S$ and a subsemigroup Orientable($S$) of $S$ were introduced in "Two cancellative commutative congruences and group diagrams", Semigroup Forum (2011) 82: 338-353. Here we demonstrate that when the semigroup is in fact a group $G$, then Orientable($G$) is the commutator subgroup $[G,G]$ and $ G / \sigma_{orient}$ is the abelian quotient group $G / [G,G]$. Comment: 4 pages, 0 figures |
| Databáze: | arXiv |
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