منابع مشابه
The Conjugacy Theorems
We use the theory of differential forms, orientation, and mapping degree to prove that all maximal tori in a compact connected Lie group are conjugate. We also prove that all Lie groups are orientable, and that if G is a compact connected Lie group and T a maximal torus of G, then dim G/T is even.
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Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...
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Generalized conjugation is the action of a group on its underlying set given by (g, x) 7→ φ(g)xg, where φ : G → G is some fixed endomorphism. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if φ has a nontrivial kernel or if it is an inner automorphism, and we give a construction that allows a part...
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We consider three theorems in ergodic theory concerning a fixed aperiodic measure preserving transformation σ of a Lebesgue probability space (X,A, μ) and show that these theorems are all equivalent. Two of these results concern the existence of a partition of the space X with special properties. The third theorem asserts that the conjugates of σ are dense in the uniform topology on the space o...
متن کاملConjugacy in Thompson’s Group
We present a characterisation of conjugacy in Thompson’s group using the natural action of F on the interval [0, 1]. This characterisation completes the program begun by Brin and Squier [BS01]. Our characterisation also provides another solution to the conjugacy problem in Thompson’s group which was first solved by Guba and Sapir using diagram groups [GS97]. A number of other solutions exist du...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.2307/2037332