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On al most recognizability by spectrum of simple classical groups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 6، شماره 4، اسفند 2017، صفحه 7-33 اصل مقاله (339 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21223 | ||
| نویسنده | ||
| Alexey Staroletov* | ||
| چکیده | ||
| The set of element orders of a finite group $G$ is called the {\em spectrum}. Groups with coinciding spectra are said to be {\em isospectral}. It is known that if $G$ has a nontrivial normal soluble subgroup then there exist infinitely many pairwise non-isomorphic groups isospectral to $G$. The situation is quite different if $G$ is a nonabelain simple group. Recently it was proved that if $L$ is a simple classical group of dimension at least 62 and $G$ is a finite group isospectral to $L$, then up to isomorphism $L\leq G\leq Aut L$. We show that the assertion remains true if 62 is replaced by 38. | ||
| کلیدواژهها | ||
| Simple classical groups؛ Element orders؛ Prime graph of a finite group؛ Almost recognizable group | ||
| مراجع | ||
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