The Möbius function of the affine linear group AGL (1, Fq)

Abstract Let AGL ( 1 , F q ) denote the affine linear group of dimension one over the finite field F q . We determine the Mobius function of the lattice of subgroups of AGL ( 1 , F q ) .

[2]  E. Bender,et al.  On the Applications of Möbius Inversion in Combinatorial Analysis , 1975 .

[3]  Jacques Thévenaz,et al.  Fonction de Möbius d'un groupe fini et anneau de Burnside , 1984 .

[4]  Euler characteristics of groups: Thep-fractional part , 1975 .

[5]  Giovanni Zini.  The Möbius function of PSU(3, 22n) , 2019, Ars Math. Contemp..

[6]  G. Jones,et al.  Möbius Inversion in Suzuki Groups and Enumeration of Regular Objects , 2014 .

[7]  I. M. Isaacs,et al.  On the Möbius function of a finite group , 1989 .

[8]  G. Rota.  On the foundations of combinatorial theory I. Theory of Möbius Functions , 1964 .

[9]  Xiang-dong Hou.  Optimal binary constant weight codes and affine linear groups over finite fields , 2019, Des. Codes Cryptogr..

[10]  P. Hall,et al.  THE EULERIAN FUNCTIONS OF A GROUP , 1936 .

[11]  Herbert Pahlings,et al.  On the Möbius function of a finite group , 1993 .

[12]  E. JacquesTLhévenaz.  Permutation representations arising from simplicial complexes , 1987 .

[13]  Hanfried Lenz,et al.  Design theory , 1985 .

[14]  John Shareshian,et al.  On the Möbius Number of the Subgroup Lattice of the Symmetric Group , 1997, J. Comb. Theory, Ser. A.

[15]  Joseph P. S. Kung,et al.  Combinatorics - The Rota Way , 2009 .

[16]  Emilio Pierro,et al.  The Mobius function of the small Ree groups , 2014, Australas. J Comb..

[17]  Gholam Reza Omidi,et al.  3-Designs from PGL(2, q) , 2006, Electron. J. Comb..

[18]  Gholam Reza Omidi,et al.  3-Designs from PSL(2, q) , 2006, Discret. Math..

[20]  The MÖBius Function of Psl2(q), with Application to the Maximal Normal Subgroups of the Modular Group , 1991 .

[21]  FROM PLANAR NEARRINGS TO GENERATING BLOCKS , 2010 .