Groups with Infinite Homology
نویسندگان
چکیده
A group is said to be acyclic if its reduced homology vanishes. Many interesting classes of groups have been discovered having this property ([2] is a useful survey). This is an indication that the reduced homology carries limited information. Here we obtain information about H̃(G) for a class of groups G that includes all locally finite groups and all soluble groups of finite rank. We show that non-locally-finite groups in the class cannot be acyclic, and that in fact their reduced homology is infinite. Our main result is as follows.
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