dihedral group


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dihedral group

[dī′hē·drəl ‚grüp]
(mathematics)
The group of rotations of three-dimensional space that carry a regular polygon into itself.
References in periodicals archive ?
Since each finite Abelian group and dihedral groups are determined by their endomorphism monoids in the class of all groups (Lemmas 2.11 and 2.13), we have
Kubo, "The dihedral group as a family group," in Quantum Field Theory and Beyond, W.
Let now k > 1, and let denote the dihedral group of order 2k, and let [C.sub.k] = ([C.sub.k], [[less than or equal to].sub.k]) denote the Cambrian lattice associated with [D.sub.k], see [9].
[D.sub.n] = <a, b | [b.sup.2] = [a.sup.k] = 1, [b.sup.-1] ab = [a.sup.-1]>--the dihedral group of order n = 2k;
(5), we can conclude that N([[GAMMA].sub.1](N))/[+ or -][[GAMMA].sub.1](N) are ([2],[W.sub.13]) and ([3],[W.sub.16]), which are isomorphic to the dihedral groups [D.sub.6], [D.sub.4] for N = 13,16 respectively.
If we accept the notion of shifting perspectives as in McCabe's application of Dihedral Group Theory, then we need a means of symbolically representing the elements of each perspective and its associated body of knowledge.
For the dihedral group W = [I.sub.2](m) one easily has [I.sub.2][(m).sup.FC](q) = 1 + 2q + 2[q.sup.2] + ...
Lee [11] proved that the automorphism group of [G.sub.T](n) is the dihedral group of symmetries of a regular n-gon.
Let G be the dihedral group of order [2.sup.m] for a large m and H the (non-normal) subgroup of order 2.
The following lemma, due to Saltman, provides an elegant solution to a local-global embedding problem involving the dihedral group.
For example, in Figure 5, the q-harmonic polynomials for the dihedral group G(4, 1, 2) are given by HG[(4,1, 2).sub.q] = [L.sub.0](q).