English

First excited state with moderate rank distribution

Group Theory 2021-10-14 v1

Abstract

Evidence is provided for the existence of infinite periodic sequences of Schur sigma-groups G with commutator quotient G/G' ~ C(3^e) x C(3), e >= 7, and logarithmic order lo(G) = 10+e. With respect to their maximal subgroups H1,H2,H3;H4, they have moderate rank distribution rho(G) = (rank3(Hi/Hi')) ~ (2,2,3;3) and represent the first excited state of their punctured transfer kernel types kappa(G), which is characterized by a polarized component, e33 or (e+1)32, of the abelian quotient invariants alpha(G) = (Hi/Hi') with lo = 6+e in contrast to the ground state with lo = 4+e.

Cite

@article{arxiv.2110.06511,
  title  = {First excited state with moderate rank distribution},
  author = {Daniel C. Mayer},
  journal= {arXiv preprint arXiv:2110.06511},
  year   = {2021}
}

Comments

7 pages, 1 figure

R2 v1 2026-06-24T06:51:01.033Z