Kourovka Problem 21.150 - Rank Inequality for p-Group Extensions

For an extension $G = A \rtimes B$ of elementary abelian $p$-groups with $a \in A$ satisfying $C_B(a) = 1$, must $H = \langle a, B\rangle$ satisfy $\operatorname{rank}(Z(H) \cap H') \le \operatorname{rank}(B)$? An explicit extension violates the bound.

Result

Disproved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Group theory

Posed by

—

Year posed

2026

Years open

0y

Solved

2026-07-20

Model

Aristotle

Vendor

Harmonic

Collaborators

—

Verification

Lean-verified

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article