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VibeMathed records no statement for this problem. See erdosproblems.com for the original.

For an extension G = A rtimes B of elementary abelian p-groups with a ∈ A satisfying C_B(a) = 1, must H = ⟨ a, B⟩ satisfy rank(Z(H) ∩ H') ≤ rank(B)? An explicit extension violates the bound.

For a finite abelian group G, let Φ(G) be the absolutely convex hull of the specified trilinear kernels and Φ'(G) its restriction where the third factor depends only on x_1 + x_2. Is Φ(G) = Φ'(G)? A counterexample over Z/3Z separates the…

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

Must every connected graph satisfy the proposed upper bound on its independence number in terms of residue and largest induced-bipartite-subgraph order? The family overlineK_2r+1 ∨ (K_r sqcup K_r) violates it for every r ≥ 3.

Grothendieck asked whether every finite locally free group scheme of order n is killed by n (its n-th convolution power map equals the unit). The counterexample is an order-4 group scheme not killed by 4 (killed only by 8); since Deligne…

Does the middle-third Cantor measure admit a Fourier frame, that is, a countable set of exponentials giving two-sided frame bounds on its L^2 space? No. The Cantor measure with base b admits no Fourier frame for any odd integer b > 1,…

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

Is every weakly quasi-complete Noetherian local ring quasi-complete? Asked by D. D. Anderson in 2014. The ring A = k^p[[X, Y]][k] with k = F_p(u_1, u_2, …) is weakly quasi-complete but not quasi-complete.

Do a finite group's order together with ∑_g ∈ G φ(|g|) determine whether the group is simple? A simple and a non-simple group of order 6048 share the statistic 23984.

Must the right-relatively convex subgroups of a right-orderable nonabelian group form a sublattice of its subgroup lattice? A construction shows they need not.

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

For every connected graph G, is α(G) ≤ ⌊ b(G) - log(ecc_avg(G)) ⌋, where b(G) is the largest induced-bipartite-subgraph order? An 11-vertex counterexample - a triangle with four leaves on each of two vertices - has α = 9 against bound 8.

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

Erdős conjectured, in over a dozen papers spanning 1976 to 1997 and with a $1000 prize attached, that every finite Sidon set extends to a perfect difference set modulo p^2+p+1 for some prime p. Alexeev and Mixon establish that 1,2,4,8 is a…

Ramachandra and Natarajan conjectured a bound on the pairwise independent correlation gap in their 2025 Operations Research Letters paper. An explicit counterexample refutes it.

For A ⊆ F_p let A^* = (A+A) ∪ (AA). Sárközy conjectured that for all large primes, every set of size at least c√p has A^* = F_p-like covering behaviour. Disproved with an explicit construction from the classical cross-ratio orbit, together…