It is well known that the existence of more than two ends in the sense of J.R. Stallings for a finitely generated discrete group G can be detected on the cohomology group H1(G,R[G]), where R is either a finite field, the ring of integers or the field of rational numbers. It will be shown (cf. Theorem A*) that for a compactly generated totally disconnected locally compact group G the same information about the number of ends of G in the sense of H. Abels can be provided by dH1(G, Bi(G)), where Bi(G) is the rational discrete standard bimodule of G, and dH•(G, _) denotes rational discrete cohomology as introduced in [6].As a consequence one has that the class of fundamental groups of a finite graph of profinite groups coincides with the class of compactly presented totally disconnected locally compact groups of rational discrete cohomological dimension at most 1 (cf. Theorem B).

中文翻译：

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完全不连贯局部紧群的有理离散一阶上同调

众所周知，对于一个有限生成的离散群，存在 JR Stallings 意义上的两个以上的端点G可以在上同调群 H 上检测到1(G,R[G]）， 在哪里R是有限域、整数环或有理数域。将显示（参见定理 A*）对于紧凑生成的完全断开的局部紧群G关于端数的相同信息G在 H 的意义上，Abel 可以由 dH 提供1(G, 毕(G))，其中 Bi(G) 是有理离散标准双模G, 和 dH•(G, _) 表示 [6] 中介绍的有理离散上同调。因此，有限群的有限图的基本群的类与有理离散上同调维数的紧呈现的完全断开的局部紧群的类一致大多数 1（参见定理 B）。