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group_theory:notions:subgroups

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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)