Symmetry group: Definition from Answers.com
The group of all symmetries of a sphere O(3) is an example of this, and in
general such continuous symmetry groups are studied as Lie groups. ...
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Klein four-group: Definition from Answers.com
In 3D there are three different symmetry groups which are algebraically the ...
Another example of the Klein four-group is the multiplicative group { 1, 3, ...
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symmetric group: Definition from Answers.com
The Sylow subgroups of the symmetric groups are important examples p-groups.
.... Related answers. Is automorphism of complete graph is a symmetric group?
...
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group: Definition, Synonyms from Answers.com
Main articles: Examples of groups and Applications of group theory .... Symmetry
groups are groups consisting of symmetries of given ..... O'Connor, J.J;
Robertson, E.F. (1996), The development of group theory, http://www-groups.dcs.
st- ...
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group theory: Definition from Answers.com
These three examples are all of groups with an infinite number of elements,
..... For example, S5, the symmetric group in 5 elements, is not solvable which
.... Abstract Algebra: Theory and Applications, http://abstract.ups.edu An ...
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Point group: Definition from Answers.com
The cyclic groups, Cn (abstract group type Zn), consist of rotations by 360°/n,
and all integer multiples. For example, a four legged chair has symmetry ...
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dihedral group: Definition from Answers.com
3 Small dihedral groups; 4 The dihedral group as symmetry group in 2D and
rotation group in 3D. 4.1 Examples of 2D dihedral symmetry ...
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Galois theory: Definition from Answers.com
See the article on Galois groups for further explanation and examples. ... This
is due to the fact that for n > 4 the symmetric group Sn contains a simple, non-
cyclic, ... http://www.math.upenn.edu/~pop/Research/files-Res/Japan01.pdf ...
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Permutation group: Definition from Answers.com
Note that the group of all permutations of a set is the symmetric group; the
term permutation ... The Rubik's Cube puzzle is another example of a permutation
group. ... From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/
PermutationInversion.html ... Related answers. What are permutation groups? ...
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alternating group: Definition from Answers.com
As in the symmetric group, the conjugacy classes in An consist of elements with
the ... Examples: the two permutations (123) and (132) are not conjugates in A3,
... The group homology of the alternating groups exhibits stabilization, ...
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