Groups and Their Graphs |
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Abelian Abelian group associated ba² binary operation C₂ Cayley diagram closed paths commutative congruence motions cosets with respect counter-clockwise cycle D₂ defining relations deformed denote dihedral group dihedral group D3 distinct elements elements of G equilateral triangle example Exercise factor group finite group flip followed four-group ƒ² graph group axioms group element group G group isomorphic group of order homomorphic mapping icosahedron identity infinite cyclic group initial position integers inverse labeled Lagrange's theorem left cosets m₁ manifold mathematics modulo multiplication table non-commutative normal subgroup odd integers odd permutations one-one pairs pattern period permutations plane proper subgroups prove quaternion group reader represent representation right cosets rotation set of defining shown in Figure subgroup H subgroup of G subgroup of order subset Suppose symbols symmetric group tetrahedron tion unit element verify vertices W₁