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- W3146039763 abstract "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) We contribute to the theory of this class of groups by showing it to be closed under perfect extension with locally soluble kernel (Theorem 2.1). (3) Applications of this key result are given to two important classes of acyclic groups, namely binate groups and groups of automorphisms of large objects (Theorems 3.1, 3.4). We call a group G with no nontrivial finite-dimensional 6-representation countert-linear. For p ^ 0, we say that G is counter-p-linear ii it is counter 6-linear for every field I of characteristic p. Finally, when G is counter-p-linear for all p (or equivalently, counter-6-linear for all 6), we say that G is counter-linear. (Evidently we are considering a special case of the following. Let C be a class of groups. Then we may call a group G counter-C if G has no nontrivial homomorphic image in C A brief discussion of this general notion appears below as an appendix.)" @default.
- W3146039763 created "2021-04-13" @default.
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- W3146039763 date "1994-01-01" @default.
- W3146039763 modified "2023-09-26" @default.
- W3146039763 title "GROUPS WITH NO NONTRIVIAL LINEAR REPRESENTATIONS" @default.
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