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group_theory:notions:subgroups [2017/01/07 13:12]
jakobadmin [Subgroups]
group_theory:notions:subgroups [2017/12/06 09:33] (current)
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 A subgroup $H$ of a given group $G$ consists of elements of $G$ that have some additional property. ​ A subgroup $H$ of a given group $G$ consists of elements of $G$ that have some additional property. ​
  
-For example, the subgroup $SO(N)$ of $O(N)$ consists of all $N \times N$ matrices with determinant equal to $1$. ($O(N)$ consists of all $N \times N$ matrices $M$ that fulfil the condition $M^T M = 1$. $SO(N)$ consists of all $N \times N$ matrices $M$ that fulfil the condition ​$M^T M = 1$ **and** $\det(M) =1$.)+For example, the subgroup $SO(N)$ of $O(N)$ consists of all $N \times N$ matrices with determinant equal to $1$. ($O(N)$ consists of all $N \times N$ matrices $M$ that fulfil the condition $M^T M = 1$. $SO(N)$ consists of all $N \times N$ matrices $M$ that fulfil the conditions ​$M^T M = 1$ **and** $\det(M) =1$.)
  
 The mathematical notation to indicate that some group $H$ is a subgroup of another group $G$ is  The mathematical notation to indicate that some group $H$ is a subgroup of another group $G$ is 
group_theory/notions/subgroups.txt ยท Last modified: 2017/12/06 09:33 (external edit)