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- Homework Statement
- if G is a group and a,b belongs to G and O(a) = e , b.a =a.b^2 then find O(b) ?

- Relevant Equations
- b.a = a.b^2

hi guys

i saw this problem : if G is a group and a,b belongs to G and O(a) = e , b.a =a.b^2 then find O(b) , but i want to tackle this problem using Cayley diagrams , so my attempt is as following :

$$ba =ab^{2}$$

then i might assume b as flipping , a as rotation :

$$ fr = rf^{2}$$

then knowing that ##r^{5} = e ## i suspect that the symmetry might be associated with a pentagon , but then i am stick here because i can't figure out the other substructure associated with this ##f^{n}## flipping .

i saw this problem : if G is a group and a,b belongs to G and O(a) = e , b.a =a.b^2 then find O(b) , but i want to tackle this problem using Cayley diagrams , so my attempt is as following :

$$ba =ab^{2}$$

then i might assume b as flipping , a as rotation :

$$ fr = rf^{2}$$

then knowing that ##r^{5} = e ## i suspect that the symmetry might be associated with a pentagon , but then i am stick here because i can't figure out the other substructure associated with this ##f^{n}## flipping .

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