On Commutation Semigroups of Dihedral Groups
For G a group and g in G, we define mappings pg(G) and lg(G) from G into G by pg(x)=[x,g] and lg(x)=[g,x]. We let P(G) and L(G) denote the subsemigroups of the set of all mappings from G to G generated by {pg: g in G} and {lg: g in G}, respectively. P(G) and L(G) are called the right and left commut...
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| creator | DeWolf, Darien Edmunds, Charles Levy, Christopher |
| description | For G a group and g in G, we define mappings pg(G) and lg(G) from G into G by
pg(x)=[x,g] and lg(x)=[g,x]. We let P(G) and L(G) denote the subsemigroups of
the set of all mappings from G to G generated by {pg: g in G} and {lg: g in G},
respectively. P(G) and L(G) are called the right and left commutation semigroup
of G, respectively. In this paper we will give explicit formulas for the orders
of both P(G) and L(G) where G is a dihedral group. |
| doi_str_mv | 10.48550/arxiv.1210.2568 |
| format | Article |
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pg(x)=[x,g] and lg(x)=[g,x]. We let P(G) and L(G) denote the subsemigroups of
the set of all mappings from G to G generated by {pg: g in G} and {lg: g in G},
respectively. P(G) and L(G) are called the right and left commutation semigroup
of G, respectively. In this paper we will give explicit formulas for the orders
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pg(x)=[x,g] and lg(x)=[g,x]. We let P(G) and L(G) denote the subsemigroups of
the set of all mappings from G to G generated by {pg: g in G} and {lg: g in G},
respectively. P(G) and L(G) are called the right and left commutation semigroup
of G, respectively. In this paper we will give explicit formulas for the orders
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pg(x)=[x,g] and lg(x)=[g,x]. We let P(G) and L(G) denote the subsemigroups of
the set of all mappings from G to G generated by {pg: g in G} and {lg: g in G},
respectively. P(G) and L(G) are called the right and left commutation semigroup
of G, respectively. In this paper we will give explicit formulas for the orders
of both P(G) and L(G) where G is a dihedral group.</abstract><doi>10.48550/arxiv.1210.2568</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Rings and Algebras |
| title | On Commutation Semigroups of Dihedral Groups |
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