Groups with no nontrivial linear representations

Groups with No Nontrivial Linear Representations: Corrigenda

Professor B.A.F. Wehrfritz has kindly drawn my attention to some errors in the above paper [1]. Principally, there is an invalid assertion of complete irreducibility used in Theorem 2.1 and its corollary. Thus the expression " 1-dimensional f-representation" should be replaced by "Abelian 6-representation" in both statements. This amended conclusion is still adequate for subsequent results. In ...

Groups with No Nontrivial Linear Representations

Our aim is to initiate the study of groups G whose finite-dimensional linear representations G —* GLn(t) over a field I are all necessarily trivial. This note has three main features: (1) We survey the existing literature on such groups. Noteworthy here is the surprising interaction with the phenomenon of acyclic (homologically trivial) groups. For further discussion see Remark 1.10 below. (2) ...

Linear Representations of Finite Groups

Some Representations of Special Linear Groups

Mat r x ( F q ) o f a l l r b y r m a t r i c e s o v e r F q , b y C t h e g r o u p G L t i ( F q ) o f t h e u n i t s of M, and by S the special linear subgroup SL , (F q ) o f C . F o r a n a r b i t r a r y field F containing F q , l e t U s t a n d f o r t h e ( c o m m u t a t i v e ) p o l y n o m i a l a l g e b r a F[xl, , x r ] , a n d c o n s i d e r U g r a d e d a s u s u a l : U...

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...