dihedral group of degree 3 and order 6. It equals the symmetric group S3. It is also the smallest non-abelian group. This page illustrates many group...
18 KB (2,657 words) - 20:57, 19 July 2024
mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the...
27 KB (3,379 words) - 04:52, 19 September 2024
physics. One of the simplest examples of a non-abelian group is the dihedral group of order 6. It is the smallest finite non-abelian group. A common example...
2 KB (216 words) - 16:58, 13 July 2024
root of unity. The group Gal ( L / Q ) {\displaystyle \operatorname {Gal} (L/\mathbb {Q} )} is isomorphic to S3, the dihedral group of order 6, and...
18 KB (3,190 words) - 20:36, 19 July 2024
mathematics, the infinite dihedral group Dih∞ is an infinite group with properties analogous to those of the finite dihedral groups. In two-dimensional geometry...
6 KB (615 words) - 19:44, 23 August 2023
nonabelian symmetric group. This group is isomorphic to the dihedral group of order 6, the group of reflection and rotation symmetries of an equilateral triangle...
46 KB (6,130 words) - 06:34, 24 May 2024
the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group...
11 KB (1,337 words) - 08:48, 12 July 2024
is D3, the dihedral group of order 6. The isometry group of a two-dimensional sphere is the orthogonal group O(3). The isometry group of the n-dimensional...
4 KB (476 words) - 22:18, 4 September 2023
this group is known as the dihedral group of order 8, and is either denoted Dih4, D4 or D8, depending on the convention. This was an example of a non-abelian...
20 KB (1,789 words) - 11:12, 14 July 2024