Kourovka Problem 21.150: Counterexample to a rank bound for p-group extensions
- Mathematics
A 3-group extension G=A⋊B with elementary abelian A and B and trivial C_B(a) can have rank(Z(H)∩H′)>rank(B), where H=⟨a,B⟩.
Kourovka Problem 21.150: Counterexample to a rank bound for p-group extensions
- Mathematics
A 3-group extension G=A⋊B with elementary abelian A and B and trivial C_B(a) can have rank(Z(H)∩H′)>rank(B), where H=⟨a,B⟩.
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Read the background
A 3-group extension G=A⋊B with elementary abelian A and B and trivial C_B(a) can have rank(Z(H)∩H′)>rank(B), where H=⟨a,B⟩.
Why it matters
An explicit finite counterexample refutes the proposed inequality.
What counts as progress
A specific group theory result with documented AI mathematical work, a stated prior baseline and a checkable source.
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Kourovka Problem 21.150: Counterexample to a rank bound for p-group extensions