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Results tagged with gm.general-mathematics
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user 120914
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
10
votes
When is 4 qualitatively different than $n\leq 3$?
The word problem is decidable in every $\leq3$-manifold group, but can be undecidable in $4$-manifold groups.
6
votes
Accepted
Get the commands history from GAP system
There are three commands that will do all variations of this:
LogTo("filename.txt") will save all subsequent input and output to a file with the specified name.
InputLogTo("filename.txt") will save a …
16
votes
Theorems with many distinct proofs
The Nielsen-Schreier theorem from combinatorial group theory ought to qualify, as it is one of the most fundamental theorems of this area. It was originally proved in a restricted form by J. Nielsen i …
13
votes
Conceptual reason why the sign of a permutation is well-defined?
Obviously, there are lots of answers already, but I thought I'd give the proof of (5) as given by Jordan already in 1870 in his Traité des substitutions -- this has the benefit of being quite clear to …