Abstract
The set of element orders of a finite group G is called the spectrum. Groups with coinciding spectra are said to be 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 ≤ G ≤ Aut L. We show that the assertion remains true if 62 is replaced by 38.
Original language | English |
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Pages (from-to) | 7-33 |
Number of pages | 27 |
Journal | International Journal of Group Theory |
Volume | 6 |
Issue number | 4 |
Publication status | Published - 1 Jan 2017 |
Keywords
- Almost recognizable group
- Element orders
- Prime graph of a finite group
- Simple classical groups