Universal groups, binate groups and acyclicity
Universal groups, binate groups and acyclicity
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全群、二元群和无环性
DOI：
10.1515/9783110848397-019
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
Y. K. Leong
中科院分区：
文献类型：
--
作者：
A. Berrick;K. N. Cheng;Y. K. Leong
在[3 p85]中指出引理11.11，用于证明代数iT理论中某个泛群的无环性（平凡整数系数的同调平凡性），“用于建立许多其他群的无环性，但是，正如他们所说，是另一回事”。这部作品呈现了另一个故事。所考虑的群的关键性质是符合[3（11.11）]假设的二元（“成对排列”）结构。我们开始从理论上考虑这种结构，然后提供一个例子的列表。几乎所有的例子都是以前已知的非循环群;然而，文献中给出的论点往往是一个特设的性质，与类比的场合注意到，但没有探讨。其中一些群体在某种意义上具有普遍性。该列表中的一个新来者（因为它以前没有被描述为非循环的）是P. Hall的可数泛局部有限群。还有另一种方式使普遍性进入这一讨论。我们开始考虑在二元群中具有普遍性的群。
In [3 p85] it is stated that Lemma 11.11, used to prove the acyclicity (triviality of homology with trivial integer coefficients) of a certain universal group in algebraic iT-theory, "serves to establish the acyclicity of many other groups besides, but that, as they say, is another story". This work presents that other story. The key property of groups under consideration is a binate ("arranged in pairs") structure conforming to the hypotheses of [3 (11.11)]. We begin with a theoretical consideration of such structures and then offer a list of examples. Almost all the examples were previously known to be acyclic groups; however the arguments given in the literature tend to be of an ad hoc nature, with analogies on occasion noted though not explored. A number of these groups are universal in some sense. One newcomer to the list (in that it has not previously been described as acyclic) is P. Hall's countable universal locally finite group. There is another way in which universality enters into this discussion. We begin by considering groups which are universal among binate groups.