HiSo I'm looking at presentations.I think that I understand that

[andlook]

Hi

So I'm looking at presentations.
I think that I understand that the group that generates <a,b|a^2,b^2> is Z/2 x Z/2. But how can I find out the group, that generates other presentations such as
<a,b,c|aba^(-1)bcc>?

Thanks

 

[rasmhop]

In general it's a hard problem to identify the group that a presentation generates. Actually a quite interesting related problem in group theory is given a presentation of a group G and two words x1x2...xn and y1y2...ym, determine whether x1x2...xn=y1...ym in G. In general this is an undecidable problem, so in some cases we may not be able to tell whether we have x1...xn=y1...ym or not. As for your specific presentation I don't immediately recognize is, but sometimes fairly simple (in the everyday sense of the word) groups can have complicated presentations.