Thompson ’ s Group at 40 Years Preliminary Problem List
Thompson ’ s Group at 40 Years Preliminary Problem List
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汤普森小组 40 年初步问题清单
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通讯作者：
M. Bridson
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作者：
M. Bridson
有公共右乘子意味着<$x <$y <$a，B使得xa = yb其中x，y，a，B ∈ kG− {0}。不知道F是否满足这个条件。顺从性是否等同于具有公共权利乘数的条件，这是开放的。问题：k字段有多重要？这可能适用于一个领域，而不是另一个？你能找到一个域k使得kF有公右倍数吗？一个中间问题：右Ore条件：ZF有右分式环吗？可序性意味着ZF嵌入在除环中。是否有其他与顺从性有关的条件，而F不为人所知？
Having common right multipliers means that ∀x∀y∃a, b so that xa = yb where x, y, a, b ∈ kG− {0}. It is unknown whether F satisfies this condition. It is open whether amenability is equivalent to this condition of having common right multipliers. Question: How important is the field k? Might this work with one field but not another? Can you find a field k so that kF has common right multiples? An intermediate question: Right Ore Condition: Does ZF have a ring of right fractions? Orderability implies that ZF embeds in a division ring. Are there other conditions related to amenability which are not known for F?