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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.
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
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