normal subgroup
==Definition==
A subgroup H of a group G is termed ... ===Normal subgroup and quotient goup===
===Normal subgroups of the ... ...
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of the subgroup. In the particular case of a normal subgroup of finite index, the reductions correspond to elements of the quotient group. ... ...
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The restricted holonomy group is a normal subgroup of the holonomy group, which comprises all the linear transformations that occur as the holonomy ... ...
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Let G be a Lie group, N a normal subgroup that is also a Lie subgroup, and G/N the quotient group. Then any principal G-bundle gives rise to ... ...
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group) of M) contains a free Abelian normal subgroup of rank n and finite index
* Thus M is a finite quotient of a flat torus (using the fact ... ...
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group of positive real numbers, which is a normal subgroup of index two in the multiplicative group of all nonzero real numbers.
==Geometric properties ... ...
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