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Results tagged with gr.group-theory
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user 7206
Questions about the branch of algebra that deals with groups.
9
votes
3
answers
1k
views
First-order axiomatization of free groups
Is there a way to axiomatize [non-abelian] free groups in first-order logic using the language of groups (which contains the binary operation symbol $\cdot$, and the constant symbol $e$)?
Is there on …
- 39.8k
7
votes
Accepted
Number of torsion-free abelian groups
You can construct antichains of size $\frak c$ without using choice, you can even have them to be antichains in a stronger sense of the word: i.e. every two have a finite intersection.
The one thing …
- 39.8k
82
votes
Results from abstract algebra which look wrong (but are true)
The free group with infinitely many generators is a subgroup of the free group with two generators.
12
votes
Accepted
The Tall Tale of Terminating Transfinite Towers
Here is a relevant paper,
Kaplan, Itay; Shelah, Saharon, The automorphism tower of a centerless group without choice, Arch. Math. Logic 48, No. 8, 799-815 (2009). ZBL1192.03026.
At least for a c …
- 39.8k