Linked Questions

12
votes
4answers
3k views

The word problem for finite groups

The word problem for finite groups is decidable. Is it obvious that this is true? In particular, I'm not entirely sure about what it means for the problem to be decidable (in this case---I think I ...
14
votes
2answers
777 views

When is a group isomorphic to the infinite cyclic group?

I am learning algebra and I am a bit confused. Let's say I have a finitely presented group $G$, can anyone tell me if it is possible to find out if $G\cong \mathbb{Z}$? Thanks
5
votes
3answers
3k views

Masters' thesis in group theory [closed]

I would like some ideas on topics in group theory which would be suitable for a masters' thesis. What sort of problems would be suitable for this level? Because it is at masters' level, no original ...
10
votes
2answers
469 views

Does algorithmic unsolvability imply unsolvability in general?

I recently found out that there is no algorithm which, given an arbitrary group presentation, will determine in finite time if it represents the trivial group*. Additionally, in a lecture I recently ...
5
votes
4answers
902 views

Topics in Combinatorial Group Theory (for a short talk).

I have started course on combinatorial group theory and supposed to give a short talk/presentation. It would be really helpful if someone can suggest some good/interesting topics to cover. Thanks
4
votes
3answers
199 views

abstract algebra example book

It's very exciting when you can use the theory to solve "lower level" problems. For example, I'm looking forward to understanding why the quintic equation is not solvable. In the undergraduate ...
1
vote
2answers
637 views

Given a Cayley table, is there an algorithm to determine if it is a dihedral group?

Showing that it is a group is simple enough, but is it possible to determine if it is a dihedral group or not just by looking at the Cayley table?
2
votes
1answer
292 views

Can someone please explain the word problem (from group theory) in Calculus III layman's terms

I'd appreciate it if someone could offer a schematic explanation of the word problem from group theory in terms which someone at a calculus III level (but without any background in group theory or ...
6
votes
0answers
780 views

Is there a classification of infinite simple groups?

The classification of finite simple groups is known to be very very long. But I was wondering: is there somehow a classification of the infinite simple groups, or at least a beginning of a ...
3
votes
3answers
307 views

Is there a simple way to distinguish between group homomorphisms?

More precisely, I am given a function $f:G\to H$ with the promise that it is a homomorphism. Is there an easy way to determine which homomorphism it is without looking through all of its values? For ...
2
votes
2answers
67 views

Inequalities in groups.

I learnt that $(\mathbb{R},\times) < (\mathbb{C},\times)$, Which means the first is a subgroup of the second one. But in the first group inequality is defined, while it's not in the latter. This ...