On complete decompositions of dihedral groups
Let G be a finite non-abelian group and B1, …, Bt be nonempty subsets of G for integer t ≥ 2. Suppose that B1, …, Bt are pairwise disjoint, then (B1, …, Bt) is called a complete decomposition of G of order t if the subset product Bi1 … Bit = {bi1 … bit | bij ∈ Bij, j = 1,2, …,t} coincides with G, wh...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2021-01-01
|
| Series: | ITM Web of Conferences |
| Online Access: | https://www.itm-conferences.org/articles/itmconf/pdf/2021/01/itmconf_icmsa2021_03001.pdf |
| _version_ | 1818930642374623232 |
|---|---|
| author | Chen Huey Voon Sin Chang Seng |
| author_facet | Chen Huey Voon Sin Chang Seng |
| author_sort | Chen Huey Voon |
| collection | DOAJ |
| description | Let G be a finite non-abelian group and B1, …, Bt be nonempty subsets of G for integer t ≥ 2. Suppose that B1, …, Bt are pairwise disjoint, then (B1, …, Bt) is called a complete decomposition of G of order t if the subset product Bi1 … Bit = {bi1 … bit | bij ∈ Bij, j = 1,2, …,t} coincides with G, where {Bi1 … Bit} = {B1, …, Bt} and the Bij are all distinct. Let D2n = ‹r,s| rn = s2 = 1, rs =srn-1› be the dihedral group of order 2n for integer n ≥3. In this paper, we shall give the constructions of the complete decompositions of D2n of order t, where 2 ≤ t ≤ n. |
| first_indexed | 2024-12-20T04:03:56Z |
| format | Article |
| id | doaj.art-bd6e64bcd25b4fb1a37666bbe95150b8 |
| institution | Directory Open Access Journal |
| issn | 2271-2097 |
| language | English |
| last_indexed | 2024-12-20T04:03:56Z |
| publishDate | 2021-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ITM Web of Conferences |
| spelling | doaj.art-bd6e64bcd25b4fb1a37666bbe95150b82022-12-21T19:54:06ZengEDP SciencesITM Web of Conferences2271-20972021-01-01360300110.1051/itmconf/20213603001itmconf_icmsa2021_03001On complete decompositions of dihedral groupsChen Huey Voon0Sin Chang Seng1Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul RahmanDepartment of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul RahmanLet G be a finite non-abelian group and B1, …, Bt be nonempty subsets of G for integer t ≥ 2. Suppose that B1, …, Bt are pairwise disjoint, then (B1, …, Bt) is called a complete decomposition of G of order t if the subset product Bi1 … Bit = {bi1 … bit | bij ∈ Bij, j = 1,2, …,t} coincides with G, where {Bi1 … Bit} = {B1, …, Bt} and the Bij are all distinct. Let D2n = ‹r,s| rn = s2 = 1, rs =srn-1› be the dihedral group of order 2n for integer n ≥3. In this paper, we shall give the constructions of the complete decompositions of D2n of order t, where 2 ≤ t ≤ n.https://www.itm-conferences.org/articles/itmconf/pdf/2021/01/itmconf_icmsa2021_03001.pdf |
| spellingShingle | Chen Huey Voon Sin Chang Seng On complete decompositions of dihedral groups ITM Web of Conferences |
| title | On complete decompositions of dihedral groups |
| title_full | On complete decompositions of dihedral groups |
| title_fullStr | On complete decompositions of dihedral groups |
| title_full_unstemmed | On complete decompositions of dihedral groups |
| title_short | On complete decompositions of dihedral groups |
| title_sort | on complete decompositions of dihedral groups |
| url | https://www.itm-conferences.org/articles/itmconf/pdf/2021/01/itmconf_icmsa2021_03001.pdf |
| work_keys_str_mv | AT chenhueyvoon oncompletedecompositionsofdihedralgroups AT sinchangseng oncompletedecompositionsofdihedralgroups |