In this chapter we will explore a few families of groups, some of which we are already familiar with.
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4.1: Cyclic Groups
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4.2: Dihedral Groups
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We can think of finite cyclic groups as groups that describe rotational symmetry. In particular, Rn is the group of rotational symmetries of a regular n -gon. Dihedral groups are those groups that describe both rotational and reflectional symmetry of regular n -gons.
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4.3: Symmetric Groups
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In general, the symmetric group on n objects is the set of permutations that rearranges the n objects. The group operation is composition of permutations.
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4.4: Alternating Groups
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