Let G be a group and let H be a subgroup of G. For any g...

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Let G be a group and let H be a subgroup of G. For any g = G, define the set gHg¹= {ghg¹|he H}. 1. Prove that gHg¹ is a subgroup of G. 2. Let (G,) be the group with the following Cayley table. I e a b С Р 9 T 8 e e a a b a b C C e Р 8 9 T b b 8 T с e a T Р 8 9 Р 9 C Р 9 Р 9 9 T a T b 8 9 e T a C e 8 Р T T 8 S P P 9 C b S с S Р 9 T a b e bae с C b a e (a) Let H = {e, p}. Identify the elements of the subgroup aHa-¹. (b). Lot K Let G be a group and let H be a subgroup of G. For any g = G, define the set gHg¹= {ghg¹|he H}. 1. Prove that gHg¹ is a subgroup of G. 2. Let (G,) be the group with the following Cayley table. I e a b С Р 9 T 8 e e a a b a b C C e Р 8 9 T b b 8 T с e a T Р 8 9 Р 9 C Р 9 Р 9 9 T a T b 8 9 e T a C e 8 Р T T 8 S P P 9 C b S с S Р 9 T a b e bae с C b a e (a) Let H = {e, p}. Identify the elements of the subgroup aHa-¹. (b). Lot K

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Given that G be a group and I be a subgroup H of G For any gG define the set gitg gngh... View the full answer