FINITE METACYCLIC GROUPS WITH FAITHFUL IRREDUCIBLE REPRESENTATIONS
نویسندگان
چکیده
منابع مشابه
QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...
متن کاملComputing Irreducible Representations of Finite Groups
We consider the bit-complexity of the problem stated in the title. Exact computations in algebraic number fields are performed symbolically. We present a polynomial-time algorithm to find a complete set of nonequivalent irreducible representations over the field of complex numbers of a finite group given by its multiplication table. In particular, it follows that some representative of each equ...
متن کاملIrreducible Representations of Finite Spin Groups
In this paper we present a computation (done by the author in 1983) which yields a multiplicity one statement for the irreducible representations of a finite spin group which, in turn, yields the classification of the irreducible representations of a finite spin group. Introduction 0.1. Let G be a connected reductive group defined over a finite field Fq and let F : G → G be the corresponding Fr...
متن کاملOn Minimal Faithful Permutation Representations of Finite Groups
The minimal faithful permutation degree n(G) of a finite group G is the least positive integer n such that G is isomorphic to a subgroup of the symmetric group Sn. Let AT be a normal subgroup of a finite group G. We prove that n(G/N) $C /i(G) if G/N has no nontrivial Abelian normal subgroup. There is an as yet unproved conjecture that the same conclusion holds if G/N is Abelian. We investigate ...
متن کاملquasi-permutation representations of metacyclic 2-groups
by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Korean Mathematical Society
سال: 2003
ISSN: 1015-8634
DOI: 10.4134/bkms.2003.40.2.177