Outer automorphisms of groups
نویسندگان
چکیده
منابع مشابه
Outer Automorphisms of Locally Finite p-Groups∗
Every group is an outer automorphism group of a locally finite p-group. This extends an earlier result [3] about countable outer automorphism groups. It is also in sharp contrast to results concerning the existence of outer automorphisms of nilpotent groups in [6, 13, 14].
متن کاملOuter automorphisms of free Burnside groups
In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelian subgroups.
متن کاملParageometric Outer Automorphisms of Free Groups
We study those fully irreducible outer automorphisms φ of a finite rank free group Fr which are parageometric, meaning that the attracting fixed point of φ in the boundary of outer space is a geometric R-tree with respect to the action of Fr, but φ itself is not a geometric outer automorphism in that it is not represented by a homeomorphism of a surface. Our main result shows that the expansion...
متن کاملThe Existence of Outer Automorphisms of Some Groups, Ii
Proof. First we consider the case where G is not abelian. Evidently there exists a normal subgroup N of G which contains the center Z of G such that G/N is cyclic of order p. Let a be an element in G such that aN generates the group G/N, and let ZN be the center of N. Clearly ZN is a normal subgroup of G, and ZSZN. The mapping : ZN-^ZN defined by <p(x) = [x, a]=xax~1a~1 is easily seen to be ...
متن کاملOuter Automorphisms of Mapping Class Groups of nonorientable Surfaces
Let Ng be the connected closed nonorientable surface of genus g ≥ 5 and Mod(Ng) denote the mapping class group of Ng . We prove that the outer automorphism group of Mod(Ng) is either trivial or Z if g is odd, and injects into the mapping class group of sphere with four holes if g is even.
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: Illinois Journal of Mathematics
سال: 1991
ISSN: 0019-2082
DOI: 10.1215/ijm/1255987976