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residuall
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There are 9 letters in RESIDUALL ( A1D2E1I1L1R1S1U1 )
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Definitions of residuall in various dictionaries:
RESIDUALL - 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...
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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 * ) * ≠ * 1. * * * * {\displaystyle 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. |