TY - JOUR

T1 - On Generators and Representations of the Sporadic Simple Groups

AU - Pellegrini, Marco Antonio

AU - Martino, L. Di

AU - Zalesski, A. E.

PY - 2014

Y1 - 2014

N2 - In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic if its characteristic and minimum polynomials coincide, and we call M almost cyclic if, for a suitable α ∈F, M is similar to diag(α·Id_h, M_1), where M_1 is cyclic and 0 ≤ h ≤ n. The paper also contains results on the generation of sporadic simple groups by minimal sets of conjugate elements.

AB - In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic if its characteristic and minimum polynomials coincide, and we call M almost cyclic if, for a suitable α ∈F, M is similar to diag(α·Id_h, M_1), where M_1 is cyclic and 0 ≤ h ≤ n. The paper also contains results on the generation of sporadic simple groups by minimal sets of conjugate elements.

KW - Eigenvalue multiplicities

KW - Irreducible representation

KW - Sporadic simple groups

KW - Eigenvalue multiplicities

KW - Irreducible representation

KW - Sporadic simple groups

UR - http://hdl.handle.net/10807/55557

U2 - 10.1080/00927872.2012.729629

DO - 10.1080/00927872.2012.729629

M3 - Article

VL - 42

SP - 880

EP - 908

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -