发表机构
North Dakota State University（北达科他州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了单关系群满足Margulis-Soifer二分法，即每个单关系群要么几乎可解，要么有无限指数的极大子群，并给出相关例子及Frattini子群的平凡性结果。
AI 中文摘要
我们建立了单关系群的Margulis-Soifer二分法：每个单关系群要么是几乎可解的，要么具有无限指数的极大子群。我们还给出了具有和不具有无限指数自由极大子群的单关系群的例子，以及同时具有自由和非自由无限指数极大子群的例子。此外，对所有不可解的单关系群，我们还证明了其Frattini子群的平凡性。我们在论文末尾附上了一个简短的问题列表。
英文摘要
We establish the Margulis-Soifer dichotomy for one-relator groups: every one-relator group is either virtually solvable or has a maximal subgroup of infinite index. We also present examples of one-relator groups with and without free maximal subgroups of infinite index, as well as examples that possess both free and non-free infinite index maximal subgroups. Triviality of the Frattini subgroup is also shown for all non-solvable one-relator groups. We close the paper with a short list of questions.
CommentsWe added a reference, corrected several symbol or word typos, and clarified the argument in Section 5 (Case 2)
