Recognition of simple groups \(B_p(3)\) by the set of element orders. (Q606017)

Let \(G\) be a finite group. The set of element orders of \(G\) is denoted by \(\omega(G)\) and is called the spectrum of \(G\). Given a natural number \(k\), a group \(G\) is said to be \(k\)-recognizable by spectrum if there are \(k\) non-isomorphic groups \(H\) such that \(\omega(H)=\omega(G)\). If \(k=1\), the group \(G\) is called recognizable by spectrum. In the present paper the authors consider the simple group \(B_p(3)\), where \(p\) is an odd prime, and prove that if \(p>3\) then the group \(B_p(3)\) is recognizable by spectrum and if \(p=3\), then \(B_3(3)\) is 2-recognizable by spectrum.