Skip to main content
MathOverflow

Return to Question

spacing; very minor change
Source Link
Goldstern
Goldstern
  • 14k
  • 1
  • 47
  • 71

Let $X_G$ be the number of normal subgroups of a group $G$. Are there examples of finitely generated groups $G$ where it is consistent to have $\aleph_0<X_G<2^{\aleph_0}$ normal subgroups? Also are there examples where $\aleph_0<X_G/\sim<2^{\aleph_0}$$\aleph_0<X_G/\mathord\sim<2^{\aleph_0}$ where $N \sim M \iff G/N \cong G/M$?

Let $X_G$ be the number of normal subgroups of a group $G$. Are there examples of finitely generated groups $G$ where it is consistent to have $\aleph_0<X_G<2^{\aleph_0}$ normal subgroups? Also are there examples where $\aleph_0<X_G/\sim<2^{\aleph_0}$ where $N \sim M \iff G/N \cong G/M$?

Let $X_G$ be the number of normal subgroups of a group $G$. Are there examples of finitely generated groups $G$ where it is consistent to have $\aleph_0<X_G<2^{\aleph_0}$ normal subgroups? Also are there examples where $\aleph_0<X_G/\mathord\sim<2^{\aleph_0}$ where $N \sim M \iff G/N \cong G/M$?

Source Link
user35370
user35370

Finitely generated group with $\aleph_0<X_G<2^{\aleph_0}$ normal subgroups?

Let $X_G$ be the number of normal subgroups of a group $G$. Are there examples of finitely generated groups $G$ where it is consistent to have $\aleph_0<X_G<2^{\aleph_0}$ normal subgroups? Also are there examples where $\aleph_0<X_G/\sim<2^{\aleph_0}$ where $N \sim M \iff G/N \cong G/M$?