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 (3,380 words) - 04:52, 10 May 2024 |
four-group is the smallest non-cyclic group. It is, however, an abelian group, and isomorphic to the dihedral group of order (cardinality) 4, symbolized... 10 KB (1,193 words) - 00:14, 7 May 2024 |
In mathematics, the quasi-dihedral groups, also called semi-dihedral groups, are certain non-abelian groups of order a power of 2. For every positive... 5 KB (623 words) - 23:46, 13 December 2022 |
generalized dihedral groups are a family of groups with algebraic structures similar to that of the dihedral groups. They include the finite dihedral groups, the... 6 KB (875 words) - 19:34, 19 March 2023 |
symmetry group. the group generated by all translations and reflections in points; they are isomorphic with the generalized dihedral group Dih(R). Up... 17 KB (2,283 words) - 19:34, 22 March 2024 |
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 (2,658 words) - 04:10, 19 April 2024 |
wrote "a3b" as a shorthand for a3 ∘ b. In mathematics this group is known as the dihedral group of order 8, and is either denoted Dih4, D4 or D8, depending... 20 KB (1,788 words) - 18:52, 17 September 2023 |
longitudinal dihedral angle of a fixed-wing aircraft Dihedral group, the group of symmetries of the n-sided polygon in abstract algebra Also Dihedral symmetry... 857 bytes (147 words) - 15:41, 30 October 2023 |
Semidirect product (category Group products) are non-abelian groups: the dihedral group of order 16 the quasidihedral group of order 16 the Iwasawa group of order 16 If a given group is a semidirect... 30 KB (4,534 words) - 05:57, 9 April 2024 |
the dihedral group of order 2n (often the notation Dn or D2n is used) K4: the Klein four-group of order 4, same as Z2 × Z2 and Dih2 D2n: the dihedral group... 33 KB (1,313 words) - 04:08, 31 October 2023 |
geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group that as... 8 KB (800 words) - 03:07, 4 March 2023 |
explains the name dihedral group. An object having symmetry group Cn, Cnh, Cnv or S2n has rotation group Cn. An object having symmetry group Dn, Dnh, or Dnd... 60 KB (5,081 words) - 08:51, 11 February 2024 |
S3 is the first nonabelian symmetric group. This group is isomorphic to the dihedral group of order 6, the group of reflection and rotation symmetries... 46 KB (6,126 words) - 06:47, 15 April 2024 |
G is an extension of a finite group by either the infinite cyclic group or the infinite dihedral group. "Cyclic group", Encyclopedia of Mathematics,... 36 KB (4,113 words) - 05:34, 9 March 2024 |
Cycle index (section Dihedral group Dn) Z(C_{n})={\frac {1}{n}}\sum _{d|n}\varphi (d)a_{d}^{n/d}.} The dihedral group is like the cyclic group, but also includes reflections. In its natural action,... 27 KB (5,007 words) - 14:06, 30 November 2023 |
In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of... 17 KB (2,234 words) - 15:40, 2 June 2023 |
In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it... 10 KB (1,428 words) - 14:39, 1 May 2024 |
In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold, such that group multiplication and taking inverses... 64 KB (9,440 words) - 19:52, 2 March 2024 |
inversion in the origin: the group of all translations and inversion in all points; this is the generalized dihedral group of R3, Dih(R3). E(1), E(2),... 16 KB (2,119 words) - 19:00, 18 December 2023 |