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searching for Outer automorphism group 13 found (80 total)

alternate case: outer automorphism group

Automorphism group of a free group (368 words) [view diff] exact match in snippet view article find links to article

of a free group. The quotient by the inner automorphisms is the outer automorphism group of a free group, which is similar in some ways to the mapping class

Simple Lie group (2,262 words) [view diff] exact match in snippet view article find links to article

subgroups of this fundamental group (modulo the action of the outer automorphism group). Simple Lie groups are fully classified. The classification is

Automorphism of a Lie algebra (714 words) [view diff] exact match in snippet view article find links to article

^{0}({\mathfrak {g}})} is known as the outer automorphism group. It is known that the outer automorphism group for a simple Lie algebra g {\displaystyle

E8 (mathematics) (6,107 words) [view diff] exact match in snippet view article

compact subgroup the compact form (see below) of E8, and has an outer automorphism group of order 2 generated by complex conjugation. As well as the complex

Almost simple group (350 words) [view diff] exact match in snippet view article find links to article

a corollary of the classification of finite simple groups, the outer automorphism group of a finite simple group is a solvable group. Thus a finite almost

Automorphisms of the symmetric and alternating groups (3,187 words) [view diff] exact match in snippet view article find links to article

automorphisms, not four. However, when A6 is viewed as PSL(2, 9) the outer automorphism group has the expected order. (For sporadic groups – i.e. those not falling

Relatively hyperbolic group (868 words) [view diff] exact match in snippet view article find links to article

hyperbolic with respect to any subgroup. The automorphism group and the outer automorphism group of a free group of finite rank at least 3 are not relatively hyperbolic

Hyperfinite type II factor (499 words) [view diff] exact match in snippet view article find links to article

infinite dimensional factor contained in R is isomorphic to R. The outer automorphism group of R is an infinite simple group with countable many conjugacy

2E6 (mathematics) (435 words) [view diff] exact match in snippet view article

abelian group of order 4 is a subgroup of the monster group. The outer automorphism group has order (3, q + 1) · f where q2 = pf. Over the real numbers,

Co-Hopfian group (1,533 words) [view diff] exact match in snippet view article find links to article

239–256 Yann Ollivier, and Daniel Wise, Kazhdan groups with infinite outer automorphism group. Transactions of the American Mathematical Society 359 (2007),

Dynkin diagram (5,608 words) [view diff] exact match in snippet view article find links to article

correspond to outer automorphisms of the Lie algebra, meaning that the outer automorphism group Out = Aut/Inn equals the group of diagram automorphisms. The diagrams

Hyperbolic metric space (3,149 words) [view diff] exact match in snippet view article find links to article

Similarly, the hyperbolicity of certain graphs associated to the outer automorphism group Out(Fn) has led to new results on this group. Negatively curved

Character table (3,536 words) [view diff] exact match in snippet view article find links to article

is connected to Dirichlet characters and Fourier analysis. The outer automorphism group acts on the character table by permuting columns (conjugacy classes)