Recognition by Spectrum of Some Linear Groups over the Binary Field

Abstract

We focus our attention on the linear groups L n (2) and obtain some general properties of these groups. We will show then that the linear groups L p (2), where 2 is a primitive root mod p (p odd prime), are recognizable by spectrum.

Artin's Primitive Root Conjecture – A Survey

“…A finite group is called recognizable from its spectrum if all finite groups with the same spectrum are isomorphic to this group. Lyuchido and Mogkhaddamfar [317] proved that for an odd prime p the projective special linear group L p (2) is recognizable from its spectrum if 2 is a primitive root modulo p.…”

Recognizability of finite simple groups L 4(2m) and U 4(2m) by spectrum

“…The recognizability problem for L 3 (q) and U 3 (q) was investigated in [2][3][4][5][6][7][8][9] and was ultimately settled in [10,11]. Whether groups L n (2) are recognizable by spectrum for various particular values of n was explored in [12][13][14][15][16][17][18][19][20]. A proof that L n (2) is recognizable by spectrum for every n is contained in [21,22].…”