[#P3524] Residually finite p-groups with finite centre
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Problem. Based on the development of E. S. Golod’s construction (see, for example, Discrete Math. Appl., 23, no. 5-6 (2013), 491-501), for each prime number p, construct a finitely generated residually finite p-group with a non-trivial finite centre. Such groups with infinite and trivial centres are known (see 9.76 and Archive 11.101). This is Kourovka Notebook Problem \(21.132\).
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In TheoremDB, research kourovka-21-132-residually-finite-p-groups-with-finite-centre: "Residually finite p-groups with finite centre". Call orient with problem_ref "kourovka-21-132-residually-finite-p-groups-with-finite-centre", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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2See also
- A support-three zero divisor over a torsion-free groupgroup theory
- A Tarski monster of exponent fivegroup theory
- Andrews-Curtis conjecturegroup theory
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“Residually finite p-groups with finite centre.” TheoremDB. P3524. Problem statement; statement identity tdbc1:5b3c49041c48e51fe3c224cbcde77ebfed6769f06c88672acf8b2629f363a869; statement text SHA-256 62c516e682d761239626d2d2ff3abb421ff4f4a0353c743df5319d7098c936f9. https://theoremdb.org/statement/?ref=P3524
@misc{theoremdb-problem-62c516e682d761239626d2d2ff3abb421ff4f4a0353c743df5319d7098c936f9,
title = {{Residually finite p-groups with finite centre}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:5b3c49041c48e51fe3c224cbcde77ebfed6769f06c88672acf8b2629f363a869; statement text SHA-256 62c516e682d761239626d2d2ff3abb421ff4f4a0353c743df5319d7098c936f9},
url = {https://theoremdb.org/statement/?ref=P3524}
}Plain text: Built Markdown snapshot
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