Unverified50% confidenceFactExact time
For 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.
1
Sources
50%
Confidence
Long-term
Relevance
10/14/2026
First Seen
Sources
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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).73% similarUnverifiedFor 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.60% similarUnverifiedAlthough the simple group PSL(2,8) is not solvable, it does not produce a dimension gap, showing that solvability implying no dimension gap is one-directional.57% similarUnverifiedThe Peter–Weyl theorem decomposes the space L^2(G) of square-integrable functions on a compact group into an orthogonal direct sum of subspaces spanned by the matrix coefficients of all irreducible unitary representations, with each irreducible representation appearing with a multiplicity equal to its dimension.56% similarUnverifiedFor linear, orthogonal and unitary maps on R^d or C^d, both the DS dimension and the Natarajan dimension equal d.55% similar
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