TITLE:
Recognition by Spectrum of Some Finite Simple Linear Groups over Fields of Characteristic 5
AUTHORS:
Huaiyu He
KEYWORDS:
Finite Simple Groups, Recognition, Spectrum, Gruenberg-Kegel Graph
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.10,
October
29,
2026
ABSTRACT: Let
L
be finite simple linear groups
A
p
(
5
)
with prime
p
,
ω(
G
)
denote the spectrum of a finite group
G
, i.e., the set of orders of its elements. We show that if
p>3
is prime, then any finite group
G
with
ω(
G
)=ω(
L
)
is isomorphic to
L
, where
L=
A
p
(
5
)
has disconnected Gruenberg-Kegel graph. As an immediate consequence of the known results, the recognition problem for all simple groups
A
p
(
5
)
by spectrum is completely resolved.