NSE Characterization of the Orthogonal group O_7(3)
preprint
OA: closed
CC-BY-4.0
Abstract
Let \(G\) be a group and \(\omega(G)\) be the set of element orders of \(G\). Let \(k\in \omega(G)\), \(s_{k}=|\{g\in G|o(g)=k\}|\) and \(nse(G)=\{s_{k}|k\in \omega(G) \}\). In this paper, we prove that if \(G\) is a group and \(O_{7} (3)\) is the Orthogonal simple group over \(GF(3)\) such that \(nse(G)=nse(O_{7} (3))\), then \(G\cong O_{7} (3)\).
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- europepmc
- last seen: 2026-05-19T01:45:01.086888+00:00
- unpaywall
- last seen: 2026-05-26T02:00:01.498150+00:00
License: CC-BY-4.0