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There is no group that is a union of seven proper subgroups but not a union of fewer proper subgroups
From Groupprops
History
This result was conjectured by Cohn and proved by Tomkinson, and is sometimes termed Tomkinson's theorem.
Statement
There is no group G that can be written as the union of seven proper subgroups but cannot be written as a union of fewer proper subgroups.
Related facts
- Union of two subgroups is not a subgroup unless they are comparable
- Union of three proper subgroups is the whole group implies they have index two and form a flower arrangement
- B.H.Neumann's lemma
