Recognition by spectrum of the groups \(^2D_{2^m+1}(3)\).
Let \(G\) be a finite group, and let \(\omega(G)\) denote the set of element orders of \(G\). The set \(\omega(G)\) is also called the spectrum of \(G\). For a natural number \(k\) a finite group \(G\) is called \(k\)-recognizable by spectrum if there are exactly \(k\) non-isomorphic groups \(H\) such that \(\omega(H)=\omega(G)\). If \(k=1\), the group \(G\) is called recognizable by spectrum. In the paper under review the author proves that the groups \(^2D_{2^m+1}(3)\) are recognizable by spectrum.
scientific article; zbMATH DE number 5643394
scientific article