= For b E G, a group, the inner automorphism ob: G → G is 06(x) = bxb-1. (a) * For G = D3 find $r and $M,, where R is a

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For B E G A Group The Inner Automorphism Ob G G Is 06 X Bxb 1 A For G D3 Find R And M Where R Is A 1 (134.83 KiB) Viewed 30 times

= For b E G, a group, the inner automorphism ob: G → G is 06(x) = bxb-1. (a) * For G = D3 find $r and $M,, where R is a rotation of 120° and Mi is a mirror reflection. (See Table 1.5.) (b) Prove for all b E G that $b is a group automorphism of G. (c) Find 00$c, where b, c E G. (d) Prove that the set of all inner automorphisms of G is a subgroup of Aut(G). (e) Describe $b when G is an abelian group. (f) For a general group G find and prove a condition on b so that $b is the identity automorphism. C