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arXiv 0707.0137math.LOmath.GR
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群的模型论连通分支

Model theoretic connected components of groups

Jakub Gismatullin

摘要:

本文对群的模型论连通分支作了一般性的阐述。证明了如果群G有NIP,则存在G的指数有界的最小不变子群(在某个小集合上)(定理5.3)。这个结果推广了Shelah定理。在这方面,我们也考虑乘法和加法群的一些环(包括有限域)。

英文摘要:

We give a general exposition of model theoretic connected components of groups. We show that if a group G has NIP, then there exists the smallest invariant (over some small set) subgroup of G with bounded index (Theorem 5.3). This result extends theorem of Shelah. We consider also in this context the multiplicative and the additive groups of some rings (including infite fields).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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