Let G be a group and a,b G such that (i) lal 4 lbl (ii) a 2 b 2 (iii) ba a 3 b a 1 b (iv) a b (v) G (a,b) Show that IGI 8 and G Q 8 ...

First we can use the given relations to find all the possible elements of the group G Since lal 4 we know that a can be one of four elements a a2 a3 o ...

Let G be a group and a,b G such that (i) lal = 4 = lbl;

Question:

Let G be a group and a,b ϵ G such that (i) lal = 4 = lbl; (ii) a² = b² ; (iii) ba = a³b = a^-1b; (iv) a ≠ b; (v) G = (a,b). Show that IGI = 8 and G ≅ Q₈.

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