M.Sc Thesis | |

M.Sc Student | Kofman Irena |
---|---|

Subject | On Zeros of Characters of Finite Groups |

Department | Department of Mathematics |

Supervisor | PROF. David Chillag (Deceased) |

This research deals with the zeros of characters of finite groups, and what can be said on the group from the way the zeros are spread in the charter table.

A character of a finite group *G* is a function from the
group to ** C**, the field of complex numbers.

A finite group *G* has an
infinite number of characters, but only a finite numbers of irreducible
characters, and every non-linear irreducible character vanishes on at least one
conjugacy class. We arrange the values of all irreducible characters in a
table, called the character table of? *G*.? Restricting the character
values and the way they are spread in the character table restricts the group
itself. In particular, we will restrict the number of zeros of the irreducible
characters and the way they are spread in the charter table. The number of
zeros of? an irreducible character is the number of conjugacy classes on which
it vanishes.

In the article by? D. Chillag, A. Gillio and M. Bianchi,? groups which all its irreducible non-linear characters vanishe on at most two conjugacy classes is described. Irit Orgil in her thesis has described the groups with the property that all irreducible non-linear characters, except possibly one, vanish on only one conjugacy class.

In this research we will describe
the groups with the property that all irreducible non-linear characters, exept
possibly two, vanish on only one conjugacy class, and there is at most one
irreducible non-linear character that vanishes on four or more conjugacy
classes. In addition, we will describe all solvable groups with up to
?zeros in charter table, where? *k*?
is the number of irreducible non-linear characters; and also we formulate and
prove the dual theorem to the theorem of? Irit Orgil.