Residually Finite Group
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every nontrivial element g in G there is a homomorphism h from G to a finite group, such that h(g) neq 1., There are a number of equivalent definitions: A group is residually finite if for each non-identity element in the group, there is a normal subgroup of finite index not containing that element. A group is residually finite if and only if the intersection of a...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every nontrivial element g in G there is a homomorphism h from G to a finite group, such that h(g) neq 1., There are a number of equivalent definitions: A group is residually finite if for each non-identity element in the group, there is a normal subgroup of finite index not containing that element. A group is residually finite if and only if the intersection of all its subgroups of finite index is trivial. A group is residually finite if and only if the intersection of all its normal subgroups of finite index is trivial. A group is residually finite if and only if it can be embedded inside the direct product of a family of finite groups
