Automorphism group of a free group information

mathematical group theory, the automorphism group of a free group is a discrete group of automorphisms of a free group. The quotient by the inner automorphisms is...

of a group Presentation of a group Nielsen transformation, a factorization of elements of the automorphism group of a free group Normal form for free...

outer automorphisms, but in abelian groups all non-identity automorphisms are outer. They form another group, the automorphism group of the given group, under...

which are all conjugate by an inner automorphism). The automorphism group of Dn is isomorphic to the holomorph of Z {\displaystyle \mathbb {Z} } /n Z...

the automorphism group of An is the symmetric group Sn, with inner automorphism group An and outer automorphism group Z2; the outer automorphism comes...

the automorphisms are constrained in a certain fashion; for instance, determining the existence of a fixed-point-free automorphism (an automorphism that...

Out(Fn), the outer automorphism group of a free group on n generators Outer automorphism group, a quotient Out(G) of the automorphism group Outwood railway...

{\displaystyle 2} automorphism, inducing an automorphism in Aut ⁡ ( C / Q ) . {\displaystyle \operatorname {Aut} (\mathbb {C} /\mathbb {Q} ).} One of the most...

a group of Lie type, it is sometimes regarded as a 27th sporadic group. The Schur multiplier of the Tits group is trivial and its outer automorphism group...

mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations...

the full automorphism group of An: Aut(An) ≅ Sn. Conjugation by even elements are inner automorphisms of An while the outer automorphism of An of order 2...

forming a complete system of invariants. The automorphism group of a finite abelian group can be described directly in terms of these invariants. The theory...

count the automorphisms of a graph. Consider the cubical graph as pictured, and let G denote its automorphism group. Then G acts on the set of vertices...

Geometric Group Theory" (PDF). Question 1.15. Retrieved 17 August 2016. Formanek, E.; Procesi, C. (1992). "The automorphism group of a free group is not...

mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains...

order 2 automorphism of An; further orthogonal groups 2Dn, from the order 2 automorphism of Dn; the new series 2E6, from the order 2 automorphism of E6; the...

GL(n, q) instead of GL(n, F). When p is prime, GL(n, p) is the outer automorphism group of the group Zpn, and also the automorphism group, because Zpn is...

Order automorphism Outer automorphism group Quotient group Examples of groups Abelian group Cyclic group Rank of an abelian group Dicyclic group Dihedral...

diagram automorphism of the general linear group (reversing the Dynkin diagram An, which corresponds to transpose inverse) and the field automorphism of the...

the automorphism group of Z × Z is GL(2, Z), the group of all 2 × 2 matrices with integer entries and determinant, ±1. This automorphism group is infinite...

\{e,{\bar {e}}\}} . The inner automorphism group of Q8 is given by the group modulo its center, i.e. the factor group Q 8 / { e , e ¯ } , {\displaystyle...

of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is mapped to itself by every automorphism of the parent group...

endomorphism of Z/nZ that maps each element to the sum of r copies of it. This is a bijection if and only if r is coprime with n, so the automorphism group of Z/nZ...

determined the automorphism group of the abstract group G(k). Every automorphism is the product of an inner automorphism, a diagonal automorphism (meaning conjugation...

isomorphism. The set of all automorphisms of a group G, with functional composition as operation, itself forms a group, the automorphism group of G. It is denoted...