# Sh:302a

- Grossberg, R. P., & Shelah, S. (1998).
*On cardinalities in quotients of inverse limits of groups*. Math. Japon.,**47**(2), 189–197. arXiv: math/9911225 MR: 1615081 -
Abstract:

Let \lambda be \aleph_0 or a strong limit of cofinality \aleph_0. Suppose that \langle G_m,\pi_{m,n}\;:\;m\leq n<\omega\rangle and \langle H_m,\pi^t_{m,n}\;:\;m\leq n<\omega\rangle are projective systems of groups of cardinality less than \lambda and suppose that for every n< \omega there is a homorphism \sigma:H_n\rightarrow G_n such that all the diagrams commute. If for every \mu< \lambda there exists \langle f_i\in G_{\omega} \;:\;i< \mu\rangle such that i\neq j\Longrightarrow f_if_j^{-1}\not\in\sigma_{\omega}(H_{\omega}) then there exists \langle f_i\in G_{\omega} \;:\;i < 2^{\lambda}\rangle such that i\neq j\Longrightarrow f_if_j^{-1}\not\in\sigma_{\omega}(H_{\omega}). - No downloadable versions available.

Bib entry

@article{Sh:302a, author = {Grossberg, Rami P. and Shelah, Saharon}, title = {{On cardinalities in quotients of inverse limits of groups}}, journal = {Math. Japon.}, fjournal = {Mathematica Japonica}, volume = {47}, number = {2}, year = {1998}, pages = {189--197}, issn = {0025-5513}, mrnumber = {1615081}, mrclass = {20E18}, note = {\href{https://arxiv.org/abs/math/9911225}{arXiv: math/9911225}}, arxiv_number = {math/9911225} }