Intersection of kernels of bihomomorphisms: Difference between revisions
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| [[Stronger than::abelian-quotient subgroup]] || || || || {{intermediate notions short|abelian-quotient subgroup|intersection of kernels of bihomomorphisms}} | | [[Stronger than::abelian-quotient subgroup]] || || || || {{intermediate notions short|abelian-quotient subgroup|intersection of kernels of bihomomorphisms}} | ||
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| [[Stronger than::completely divisibility-closed subgroup]] || || || || {{intermediate notions short|completely divisibility-closed subgroup|intersection of kernels of bihomomorphisms}} | | [[Stronger than::completely divisibility-closed subgroup]] || || [[intersection of kernels of bihomomorphisms implies completely divisibility-closed]] || || {{intermediate notions short|completely divisibility-closed subgroup|intersection of kernels of bihomomorphisms}} | ||
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| [[Stronger than::completely divisibility-closed normal subgroup]] || || || || {{intermediate notions short|completely divisibility-closed normal subgroup|intersection of kernels of bihomomorphisms}} | | [[Stronger than::completely divisibility-closed normal subgroup]] || || follows from [[intersection of kernels of bihomomorphisms implies completely divisibility-closed]] || || {{intermediate notions short|completely divisibility-closed normal subgroup|intersection of kernels of bihomomorphisms}} | ||
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Latest revision as of 06:11, 28 March 2013
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
Definition
A subgroup of a group is termed an intersection of kernels of bihomomorphisms if we can write where each is a kernel of a bihomomorphism.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| kernel of a bihomomorphism | ||||
| kernel of a multihomomorphism |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| abelian-quotient subgroup | |FULL LIST, MORE INFO | |||
| completely divisibility-closed subgroup | intersection of kernels of bihomomorphisms implies completely divisibility-closed | |FULL LIST, MORE INFO | ||
| completely divisibility-closed normal subgroup | follows from intersection of kernels of bihomomorphisms implies completely divisibility-closed | |FULL LIST, MORE INFO |