Question

Need help understanding the concept:
In group theory, the associativity rule says: m: G x G --> G, and i: G--> G where m: multiplication and i: inverse
For every g, h, and k in G,
m(m(g, h), k) =m (g, m(h, k)
and for every g in G, m(g,i(g)) =e=m(i(g),g)
Please explain me

Answer 1

@ganeshie8 give me example, please

Answer 2

i have no clue sorry :(
@zzr0ck3r

Answer 3

Thanks but wonder why!! is it not group theory which you master ??

Answer 4

I have taken number theory before... i won't be useful here really sorry

Answer 5

oh, number theory is different from group theory, hihihi... Thanks for reply.

Answer 6

m: G x G --> G
that says "m" takes two input, each from G, and produces an output which is in G

m(m(g, h), k) =m (g, m(h, k)
is notation that means the same thing as
(g*h) * k = g * (h*k)

(which is the associative property)

Answer 7

oh, I go it, thank you very much. the same with the second one, Let me interpret it
multiplication between g and its inverse = multiplication between g inverse and g,
am I right?

Answer 8

it's obviously more abstract than "times", because we don't (yet) have definition of "m", i.e. how it maps G x G to G

Answer 9

Yes, but the second statement
m(g,i(g)) =e=m(i(g),g)
looks more like the commutative property.
However, they are saying its the associative property, so there must be a way to interpret it that way.

Answer 10

and e is identity element in the group. right?

Answer 11

yes, it must be (by definition, a*i(a) = identity )

Answer 12

oh, it makes sense now. Thank you so much.

Answer 13

yw