论文标题
从牙套到前戒指
From braces to pre-Lie rings
论文作者
论文摘要
令$ a $为基数的支撑$ p^{n} $，其中$ p> n+1 $是PRIME，然后让$ ann（p^{2}）$是该撑杆中最多$ p^{2} $的元素元素。我们构建了一个与支撑$ A/ANN（P^{2}）$相关的预圈环。 如果强烈的nilpotent指数nilpotent Braces $ k <p $ brace $ a/ann（p^{2}）$可以通过将一组流量的构造施加到由此产生的前lie戒指上来回收。我们不知道，当应用于不正确的nilpotent的牙套时，我们的构造与流量群有关。我们在研究固定点很少的支架自动形态学的研究中，使用与有限$ p $ group相关的强大谎言环。作为一个应用程序，我们绑定了撑杆中用给定元素通勤的元素的数量，以及从左侧乘以给定元素乘以零的元素的数量，给出了零。 我们还研究了与强大的群体和牙套相关的各种谎言，它们的伴随组很强大，并表明获得的谎言和前戒指也很强大。 我们还表明，其伴随组具有强大且强大的左Nilpotent Pre-lie戒指的牙套是一对一的信件，并且在某些基数假设下它们是左而右的。
Let $A$ be a brace of cardinality $p^{n}$ where $p>n+1$ is prime, and let $ann (p^{2})$ be the set of elements of additive order at most $p^{2}$ in this brace. We construct a pre-Lie ring related to the brace $A/ann(p^{2})$. In the case of strongly nilpotent braces of nilpotency index $k<p$ the brace $A/ann(p^{2})$ can be recovered by applying the construction of the group of flows to the resulting pre-Lie ring. We don't know whether, when applied to braces which are not right nilpotent, our construction is related to the group of flows. We use powerful Lie rings associated with finite $p$-groups in the study of brace automorphisms with few fixed points. As an application we bound the number of elements which commute with a given element in a brace, as well as the number of elements which multiplied from left by a given element give zero. We also study various Lie rings associated to powerful groups and braces whose adjoint groups are powerful, and show that the obtained Lie and pre-Lie rings are also powerful. We also show that braces whose adjoint groups are powerful and powerful left nilpotent pre-Lie rings are in one-to-one correspondence and that they are left and right nilpotent under some cardinality assumptions.
