Notes on the filtration of the K-theory for abelian p-groups
Pith reviewed 2026-05-24 17:53 UTC · model grok-4.3
The pith
Errors in earlier gamma filtration calculations for K-theory of non-elementary abelian p-groups are corrected and extended from the case p=2 to odd primes.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Errors present in the 2015 Kodai Math. J. paper on gamma filtrations for the K-theory of BG, G an abelian p-group that is not elementary, are corrected; the results of Chetard for the case p=2 are extended to odd primes.
What carries the argument
Gamma filtration on the K-theory ring of the classifying space BG for a non-elementary abelian p-group G.
If this is right
- The corrected gamma filtration yields the correct associated graded ring for the K-theory of these classifying spaces.
- The extension supplies explicit descriptions of the filtration for every odd prime p.
- Algebraic K-theory computations for BG now rest on the revised statements rather than the earlier erroneous ones.
Where Pith is reading between the lines
- The same correction procedure may apply to other filtration functors on K-theory of finite groups.
- Once the odd-prime case is settled, one can ask whether the filtration behaves uniformly across all primes.
- The corrected statements could be used to recompute specific low-dimensional examples that were previously based on the 2015 formulas.
Load-bearing premise
The mistakes diagnosed in the 2015 paper are correctly identified and the techniques that worked for p=2 carry over directly to odd primes without new obstructions.
What would settle it
An explicit computation, for a concrete non-elementary abelian p-group with odd prime, of the associated graded ring of the gamma filtration that either agrees with or contradicts the corrected formulas given here.
read the original abstract
In this paper, I correct errors in my paper (Kodai Math. J. (2015)) about gamma filtrations for classifying spaces for abelian p-groups which are not elementary. We also extend Chetard's results for such 2-groups to p-groups for odd prime.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript corrects errors identified in the author's 2015 Kodai Math. J. paper concerning the gamma filtration on the K-theory of classifying spaces BG for non-elementary abelian p-groups. It also extends Chetard's results, previously established for 2-groups, to the case of odd primes p.
Significance. If the error corrections are accurate and the extension to odd primes is rigorously justified, the work would complete the description of gamma filtrations for K(BG) across all abelian p-groups. This has value for explicit computations in topological K-theory and related spectral sequences.
major comments (1)
- The central claim includes extending Chetard's constructions for p=2 to odd primes, but the manuscript does not verify that the spectral-sequence arguments and vanishing statements remain valid without new obstructions from the odd-primary Steenrod algebra or differences in Adams operations on K(BG). This is load-bearing for the extension and requires explicit checks or additional vanishing results.
Simulated Author's Rebuttal
We thank the referee for their detailed review and for highlighting the need for explicit verification when extending the results to odd primes. We agree that this is a load-bearing aspect of the central claim and will strengthen the manuscript accordingly.
read point-by-point responses
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Referee: The central claim includes extending Chetard's constructions for p=2 to odd primes, but the manuscript does not verify that the spectral-sequence arguments and vanishing statements remain valid without new obstructions from the odd-primary Steenrod algebra or differences in Adams operations on K(BG). This is load-bearing for the extension and requires explicit checks or additional vanishing results.
Authors: We acknowledge that the current draft relies on the formal similarity of the spectral sequence arguments without spelling out the odd-primary case in full detail. The underlying computations of the gamma filtration on K(BG) for abelian p-groups proceed via the same Atiyah-Hirzebruch spectral sequence and Adams operations used by Chetard, and the relevant vanishing statements follow from the structure of the cohomology ring H^*(BG; Z_p) together with the action of the Adams operations, which are defined uniformly for all primes. Nevertheless, to address the referee's concern we will add an explicit subsection (new Section 4.3) that verifies: (i) the odd-primary Steenrod algebra does not introduce additional differentials or extensions that obstruct the filtration computation, (ii) the Adams operations on K(BG) satisfy the same commutation relations with the filtration as in the p=2 case, and (iii) the vanishing of the relevant E_2-page terms holds verbatim for odd p by the same algebraic arguments on the symmetric algebra. These checks will be carried out using the known description of the mod-p cohomology of abelian p-groups and the standard properties of the Adams operations in topological K-theory. revision: yes
Circularity Check
No circularity: paper corrects own prior work and extends external results without load-bearing self-derivation
full rationale
The paper's stated purpose is to correct errors identified in the author's own 2015 paper and to extend Chetard's (external) results on 2-groups to odd primes. No derivation chain is presented in which a claimed prediction or uniqueness result reduces by construction to a fitted parameter, self-defined quantity, or unverified self-citation. The self-reference is explicitly corrective rather than justificatory, and the extension step is framed as an adaptation of independent prior work. No equations, ansatzes, or uniqueness theorems are invoked that collapse to the paper's own inputs.
discussion (0)
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