Sylow-centralizing sections of outer automorphism groups of finite groups are nilpotent

1975 ◽  
Vol 141 (1) ◽  
pp. 57-76 ◽  
Author(s):  
Everett C. Dade
Keyword(s):  
Finite Groups ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Outer Automorphism Groups

On coleman outer automorphism groups of finite groups

2014 ◽  
Vol 34 (3) ◽  
pp. 790-796 ◽  
Author(s):  
Jinke HAI ◽  
Zhengxing LI
Keyword(s):  
Finite Groups ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Outer Automorphism Groups

Farrell cohomology and centralizets of elementary abelian p-subgroups

1996 ◽  
Vol 119 (3) ◽  
pp. 403-417 ◽  
Author(s):  
Chun-Nip Lee
Keyword(s):  
Finite Groups ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Cohomological Dimension ◽  
Finite Graph ◽  
Mapping Class ◽  
Torsion Free Subgroup ◽  
Outer Automorphism Groups ◽  
Virtual Cohomological Dimension ◽  
Torsion Free

Let Γ be a discrete group. Γ is said to have finite virtual cohomological dimension (vcd) if there exists a finite index torsion-free subgroup Γ′ of G such that Γ′ has finite cohomological dimension over ℤ. Examples of such groups include finite groups, fundamental group of a finite graph of finite groups, arithmetic groups, mapping class groups and outer automorphism groups of free groups. One of the fundamental problems in topology is to understand the cohomology of these finite vcd-groups.

The finite inner automorphism groups of division rings

1995 ◽  
Vol 118 (2) ◽  
pp. 207-213 ◽  
Author(s):  
M. Shirvani
Keyword(s):  
Finite Groups ◽  
Galois Theory ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Commutative Field ◽  
Division Rings ◽  
Inner Automorphism ◽  
Projective Representations ◽  
Inner Automorphisms ◽  
A Finite Group

Let G be a finite group of automorphisms of an associative ring R. Then the inner automorphisms (x↦ u−1xu = xu, for some unit u of R) contained in G form a normal subgroup G0 of G. In general, the Galois theory associated with the outer automorphism group G/G0 is quit well behaved (e.g. [7], 2·3–2·7, 2·10), while little group-theoretic restriction on the structure of G/G0 may be expected (even when R is a commutative field). The structure of the inner automorphism groups G0 does not seem to have received much attention so far. Here we classify the finite groups of inner automorphisms of division rings, i.e. the finite subgroups of PGL (1, D), where D is a division ring. Such groups also arise in the study of finite collineation groups of projective spaces (via the fundamental theorem of projective geometry, cf. [1], 2·26), and provide examples of finite groups having faithful irreducible projective representations over fields.

scholarly journals Outer automorphism groups of metabelian groups

2000 ◽  
Vol 149 (3) ◽  
pp. 251-266 ◽  
Author(s):  
Rüdiger Göbel ◽  
Agnes T. Paras
Keyword(s):  
Automorphism Groups ◽  
Outer Automorphism ◽  
Metabelian Groups ◽  
Outer Automorphism Groups

scholarly journals OUTER AUTOMORPHISM GROUPS OF CERTAIN TREE PRODUCTS OF ABELIAN GROUPS

2008 ◽  
Vol 77 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Y. D. CHAI ◽  
YOUNGGI CHOI ◽  
GOANSU KIM ◽  
C. Y. TANG
Keyword(s):  
Automorphism Groups ◽  
Abelian Groups ◽  
Outer Automorphism ◽  
Finitely Generated ◽  
Residually Finite ◽  
Outer Automorphism Groups

AbstractWe prove that certain tree products of finitely generated Abelian groups have Property E. Using this fact, we show that the outer automorphism groups of those tree products of Abelian groups and Brauner’s groups are residually finite.

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