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Finite subnormal subgroup

1,252 bytes added, 22:03, 12 May 2010
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===Stronger properties===
* {| class="wikitable" border="1"! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions|-| [[Weaker than::Finite characteristic subgroup]]| the subgroup is both a [[finite group]] and a [[characteristic subgroup]] || || (characteristic implies subnormal, via normal) || use [[normal not implies characteristic]] (finite examples) || {{intermediate notions short|finite subnormal subgroup|finite characteristic subgroup}}* |-| [[Weaker than::Finite normal subgroup]]|| the subgroup is both a [[finite group]] and a [[normal subgroup]] || (normal implies subnormal) || [[normality is not transitive]] (finite examples) || {{intermediate notions short|finite subnormal subgroup|finite normal subgroup}}|-| [[Weaker than::Subnormal subgroup of finite group]] || [[subnormal subgroup]] where the whole group is a [[finite group]] || || || {{intermediate notions short|finite subnormal subgroup|subnormal subgroup of finite group}}|}
===Weaker properties===
* {| class="wikitable" border="1"! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions|-| [[Stronger than::Finitely generated subnormal subgroup]]|| || || || {{intermediate notions short|finitely generated subnormal subgroup|finite subnormal subgroup}}* | [[Stronger than::Subnormal subgroup]]|| || || || {{intermediate notions short|subnormal subgroup|finite subnormal subgroup}}|} 
===Related properties===
* [[Stronger than::Subnormal subgroup of finite index]]
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