Hello!!! thanks for reading!
Here's the problem (regarding groups, but nothing too complex):
I'm told that a and b are elements in G, which is a group.
I'm also told that b<>e (where e is the unit element - thus e*a = a, etc...), and that o(a) = 5 (meaning: a^5=e, and 5 is the smallest natural number that satisfies that).
I'm told that: aba^-1 = b^2
I need to find o(b).
This looks pretty innocent at first (and maybe it really is), but I've spent too much time on this question... tried every trick I know...
I've proved, some excercises before, that o(aba^-1)=o(b), so I tried using that a lot, but it didn't really get me much.
Of course I tried to do "^5" to both sides, and many many other things, playing with the inverses etc....
Best I could get, with much effort, is that o(ba) = 5.
I just don't know what to do :-\