let-a-b-be-any-two-elements-in-group-G-such-that-a-4-b-2-and-a-3-b-ab-find-ab-help-me-sir-please-

Question Number 134523 by mohammad17 last updated on 04/Mar/21

l e t a, b b e a n y t w o e l e m e n t s i n g r o u p G

s u c h t h a t ∣ a ∣= 4, ∣ b ∣= 2 a n d a^{3} b = a b

f i n d ∣ a b ∣ ?

h e l p m e s i r p l e a s e

Commented by kaivan.ahmadi last updated on 04/Mar/21

a^{4} = b^{2} = e

a^{3} b = a b \Rightarrow a^{4} b^{2} = a^{2} b^{2} \Rightarrow e = a^{2} \Rightarrow∣ a ∣= 2

s o t h e h y p o t h e s i s i s n o t t r u e .

Commented by kaivan.ahmadi last updated on 04/Mar/21

i f ∣ a ∣= 4 a n d ∣ b ∣= 2 t h e n w e h a v e

∣ a b ∣= \frac{∣ a ∣ . ∣ b ∣}{(∣ a ∣, ∣ b ∣)} = \frac{4 \times 2}{2} = 4