论文标题
具有琐碎基本组和独特的质量分解的财产（T）因素的新示例（T）因素
New examples of Property (T) factors with trivial fundamental group and unique prime factorization
论文作者
论文摘要
在本文中，我们提供了具有微不足道基本群体的财产因素的新示例（T）群体因素，从而为Popa提供了更多证据，以证明Popa关于财产（T）群体因素的基本群体的琐事（第9页\ Cite {Po13};另请参阅问题2，另请参见第551页，Connes'Book'book'book \ cite \ cite \ cite \ cite {co94}）。我们的小组是类$ \ Mathscr s $或类$ \ mathscr v $的组的直接产品，如\ cite {cdhk20}中所介绍。我们为这些产品组建立了一个独特的素数分解结果，从而为Popa对属性分解（T）因素的猜想提供了更多证据（第9页\ cite {po13}）。
In this paper we provide new examples of property (T) group factors with trivial fundamental group thereby providing more evidence towards Popa's conjecture on triviality of fundamental groups for property (T) group factors (page 9 \cite{Po13}; see also Problem 2, page 551 in Connes' book \cite{Co94}). Our groups arise as direct product of groups either in Class $\mathscr S$ or Class $\mathscr V$, as introduced in \cite{CDHK20}. We establish a unique prime factorization result for these product groups, thereby providing more evidence towards Popa's conjecture on prime decomposition of property (T) factors (page 9 \cite{Po13}).
