Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 38 min ago
PreprintarXiv licencearXiv

Finiteness properties of profinite blocks and blocks with defect group ℤpn

  • Florian Eisele
  • John W. MacQuarrie
Open at sourcePDFDOICite

Abstract

We prove that any block of a profinite group with a topologically finitely generated defect group D is isomorphic to a block of a virtually pro-p group, and if D is finitely presented then so is the basic algebra of the block over k. Using these general results we then prove that any block with defect group D=ℤpn is Morita equivalent to 𝒪α[[ℤpnrtimes E]] for a finite p'-group E acting faithfully and a $2$-cocycle α∈ H2(E,k×). In particular, Donovan's conjecture holds for such blocks of profinite groups.

Related

  1. The Lie algebra structure of HH1(B) for blocks with a normal defect group
    Markus Linckelmann, Jialin Wang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Finiteness properties of closed subgroups of Thompson's group F
    Gili Golan
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Profinite groups whose closed subgroups are subnormal of defect at most two
    A. L. P. Porto, I. Lima, M. Silva
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Infinite girth and profinite properties of residually finite groups
    Pratyush Mishra
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Homological finiteness properties of wreath products
    Laurent Bartholdi, Yves De Cornulier, Dessislava H. Kochloukova
    Quarterly Journal of MathematicsPeer-reviewedLicence not statedFull text12 citedAlgebra & number theoryHAL

Cite

BibTeXRIS
BibTeX
@misc{eisele2026finiteness,
  title = {{Finiteness properties of profinite blocks and blocks with defect group $\mathbb Z_p^n$}},
  author = {Florian Eisele and John W. MacQuarrie},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32587},
  eprint = {2609.32587},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32587},
}
RIS
TY  - UNPB
TI  - Finiteness properties of profinite blocks and blocks with defect group ℤ_p^n
AU  - Florian Eisele
AU  - John W. MacQuarrie
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32587
UR  - https://arxiv.org/abs/2609.32587
AB  - We prove that any block of a profinite group with a topologically finitely generated defect group D is isomorphic to a block of a virtually pro-p group, and if D is finitely presented then so is the basic algebra of the block over k. Using these general results we then prove that any block with defect group D=ℤ_p^n is Morita equivalent to 𝒪_α[[ℤ_p^nrtimes E]] for a finite p'-group E acting faithfully and a $2$-cocycle α∈ H^2(E,k^×). In particular, Donovan's conjecture holds for such blocks of profinite groups.
ER  -