Solving Group G Show: Very Important!

[hashimcom]

very important...

at any group G show
i)o(ab) = o(ba)
ii) o(a) = o(cac^-1) c in G

please i want solving

 

[HallsofIvy]

You need to first read the rules for this forum! What have you DONE on this problem? Where exactly did you get blocked?

To start you off, what does "o(a)" MEAN? If you know that o(a)= n, what does that tell you about a? What equation can you write?

 

[hashimcom]

NOW, o(a) means order of element a
a is element in group G

 

[NoMoreExams]

He asked for an equation relating all your things so you can possibly take the next step.

 

[HallsofIvy]

NOW, o(a) means order of element a
a is element in group G

No, that is just saying what that symbol means. What is the definition of "order of element a of group G". If I say that a, an element of group, G, has order n, what does that MEAN?

 

[hashimcom]

at any group G show
i)o(ab) = o(ba)


please i want solving

for that question i have a hent which is (( write ab=a(ba)a^-1)))

 

[hashimcom]

No, that is just saying what that symbol means. What is the definition of "order of element a of group G". If I say that a, an element of group, G, has order n, what does that MEAN?

it means a^n=e where n is the least integer satsfy last equations

 

[NoMoreExams]

it means a^n=e where n is the least integer satsfy last equations

Great now what does o(ab) mean in terms of what you just said?

 

[hashimcom]

Great now what does o(ab) mean in terms of what you just said?

is means if its finite there exist an integer n s.t. ab^n =e
but if else ; ther exest no integer s.t. ab^n =e

now we can write ab = a(ba)a^-1
then ...compleate

 

[NoMoreExams]

is means if its finite there exist an integer n s.t. ab^n =e
but if else ; ther exest no integer s.t. ab^n =e

now we can write ab = a(ba)a^-1
then ...compleate

I thought it meant that (ab)^n = e