کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6414468 | 1630491 | 2015 | 57 صفحه PDF | دانلود رایگان |
The spectrum Ï(G) of a finite group G is the set of element orders of G. Finite groups G and H are isospectral if their spectra coincide. Suppose that L is a simple classical group of sufficiently large dimension (the lower bound varies for different types of groups but is at most 62) defined over a finite field of characteristic p. It is proved that a finite group G isospectral to L cannot have a nonabelian composition factor which is a group of Lie type defined over a field of characteristic distinct from p. Together with a series of previous results this implies that every finite group G isospectral to L is 'close' to L. Namely, if L is a linear or unitary group, then L⩽G⩽AutL, in particular, there are only finitely many such groups G for given L. If L is a symplectic or orthogonal group, then G has a unique nonabelian composition factor S and, for given L, there are at most 3 variants for S (including SâL).
Journal: Journal of Algebra - Volume 423, 1 February 2015, Pages 318-374