Unverified50% confidenceFactExact time
For a finite Galois extension over a countable field, the Natarajan dimension equals the group-invariant coset-cube number, whose value is at least the number of complement factors of any chief series of any subgroup.
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10/14/2026
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Related Claims
UnverifiedFor the Galois group Sn of a general equation of degree n, the DS dimension coincides with the Natarajan dimension if and only if n ≤ 4; in the characteristic-zero case, this is equivalent to the equation being solvable by radicals (the Abel-Ruffini theorem).63% similarUnverifiedA Lie algebra is the tangent space of a Lie group at the identity element, allowing multiplication on the group to be approximated by addition in a vector space.62% similarUnverifiedAccording to the Künneth formula, the Betti numbers of a product space are determined by the product of the generating polynomials of the Betti numbers of each factor.61% similarUnverifiedFor the Galois groups A5 and S5 of the quintic equation, the DS dimension and the Natarajan dimension exhibit gaps of 2<3 and 3<4 respectively, and A5 is the smallest group for which such a gap exists.60% similarUnverifiedThe Marčenko–Pastur law states that the upper bound of the support interval for the eigenvalue distribution of a purely random matrix is λ_max = σ²(1+√q)², where q = N/T.60% similar
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