The semidirect product and the first cohomology of topological groups
نویسندگان
چکیده
منابع مشابه
First non-abelian cohomology of topological groups II
In this paper we introduce a new definition of the first non-abelian cohomology of topological groups. We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...
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in this paper we introduce a new definition of the first non-abelian cohomology of topological groups. we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...
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15 صفحه اولSemidirect product decomposition of Coxeter groups
Let (W,S) be a Coxeter system, let S = I ∪ J be a partition of S such that no element of I is conjugate to an element of J , let J̃ be the set of WI -conjugates of elements of J and let W̃ be the subgroup of W generated by J̃ . We show that W = W̃ ⋊WI and that J̃ is the canonical set of Coxeter generators of the reflection subgroup W̃ of W . We also provide algebraic and geometric conditions for an e...
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ژورنال
عنوان ژورنال: International Mathematical Forum
سال: 2007
ISSN: 1314-7536
DOI: 10.12988/imf.2007.07124