The automorphism group of the free group with two generators.
نویسندگان
چکیده
منابع مشابه
THE AUTOMORPHISM GROUP OF FINITE GRAPHS
Let G = (V,E) be a simple graph with exactly n vertices and m edges. The aim of this paper is a new method for investigating nontriviality of the automorphism group of graphs. To do this, we prove that if |E| >=[(n - 1)2/2] then |Aut(G)|>1 and |Aut(G)| is even number.
متن کاملCongruence Subgroups of the Automorphism Group of a Free Group
Let n ≥ 2 and Fn be the free group of rank n. Its automorphism group Aut(Fn) has a well-known surjective linear representation ρ : Aut(Fn) −→ Aut(Fn/F ′ n) = GLn(Z) where F ′ n denotes the commutator subgroup of Fn. By Aut (Fn) := ρ(SLn(Z)) we denote the special automorphism group of Fn. For an epimorphism π : Fn → G of Fn onto a finite group G we call Γ(G, π) := {φ ∈ Aut(Fn) | πφ = π} the stan...
متن کاملThe Automorphism Tower of a Free Group
We prove that the automorphism group of any non-abelian free group F is complete. The key technical step in the proof: the set of all conjugations by powers of primitive elements is first-order parameter-free definable in the group Aut(F ). Introduction In 1975 J. Dyer and E. Formanek [2] had proved that the automorphism group of a finitely generated non-abelian free group F is complete (that i...
متن کاملTHE AUTOMORPHISM GROUP OF NON-ABELIAN GROUP OF ORDER p^4
Let G be a finite non-abelian group of order p^4 . In this paper we give a structure theorem for the Sylow p-subgroup, Aut_p(G) , of the automorphism group of G.
متن کاملOn the Linearity of the Holomorph Group of a Free Group on Two Generators
Let Fn denote the free group generated by n letters. The purpose of this article is to show that Hol(F2), the holomorph of the free group on two generators, is linear. Consequently, any split group extension G = F2 ⋊H for which H is linear has the property that G is linear. This result gives a large linear subgroup of Aut(F3). A second application is that the mapping class group for genus one s...
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: Michigan Mathematical Journal
سال: 1960
ISSN: 0026-2285
DOI: 10.1307/mmj/1028998343