[#P12863] Common divisors of disjoint coset indices
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Problem. Let \(k>1\), let \(G\) be a group, and let \(a_1H_1,\ldots,a_kH_k\) be pairwise disjoint left cosets of subgroups of finite index in \(G\). Must there be indices \(1\leq i<j\leq k\) such that \(\gcd([G:H_i],[G:H_j])\geq k\)?
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In TheoremDB, research kourovka-20-99-sun-gcd-of-disjoint-coset-indices: "Common divisors of disjoint coset indices". Call orient with problem_ref "kourovka-20-99-sun-gcd-of-disjoint-coset-indices", 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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“Common divisors of disjoint coset indices.” TheoremDB. P12863. Problem statement; statement identity tdbc1:908b74269a4d38fa4f4efee4c588b7d75ca15f074c71070a1f80400de23b801a; statement text SHA-256 a853fd711980e41349a62fce6d8931e3c28dd9ca1f0c475211aa02803770a519. https://theoremdb.org/statement/?ref=P12863
@misc{theoremdb-problem-a853fd711980e41349a62fce6d8931e3c28dd9ca1f0c475211aa02803770a519,
title = {{Common divisors of disjoint coset indices}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:908b74269a4d38fa4f4efee4c588b7d75ca15f074c71070a1f80400de23b801a; statement text SHA-256 a853fd711980e41349a62fce6d8931e3c28dd9ca1f0c475211aa02803770a519},
url = {https://theoremdb.org/statement/?ref=P12863}
}Plain text: Built Markdown snapshot
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