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Results tagged with gr.group-theory
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user 57583
Questions about the branch of algebra that deals with groups.
4
votes
First-order axiomatization of free groups
More can be said than non-first-order axiomatizability. Since the free group $ \mathbb{Z}^{(\omega)}$ is an $L_{\infty, \omega}$-elementary substructure of the non-$\aleph_{2}$-free group $\mathbb{Z} …
- 2,111
14
votes
0
answers
517
views
Is $\mathbb{Z}^{\omega}$ ever the union of a chain of proper subgroups each isomorphic to $\...
Recall that the covering number $cov(B)$ is the least cardinal $\kappa$ such that $\kappa$ meagre sets cover the real line. Andreas Blass and John Irwin http://www.math.lsa.umich.edu/~ablass/bb.pdf pr …
- 2,111
2
votes
Ultraproducts of finite cyclic groups
I agree with the first answer.
The ultraproduct in question is pure-injective (by a theorem of Jan Mycielski, Some compactifications of general agebras, Coll. Math., 13 (1964), 1-9). If an abelian g …
- 2,111