Suppose H is a proper fact about::conjugate-permutable subgroup of ... join-closed: If H is a conjugate-permutable subgroup of G, and g ... ...
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Any conjugate-permutable subgroup of a finite group is subnormal. ... Given: A finite group G, a conjugate-permutable subgroup H of G. ... ...
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The notion of self-conjugate-permutable subgroup was introduced by ... * Conjugate-permutable subgroup: In fact, a subgroup is both conjugate ... ...
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weaker = conjugate-permutable subgroup}}
==Statement==
===Property ... The subgroup property of being a subnormal subgroup does not imply ... ...
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of being a right-transitively conjugate-permutable subgroup. to the property of being a conjugate-permutable subgroup and the property ... ...
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weaker = conjugate-permutable subgroup}}
==Statement==
===Verbal statement ... ===Conjugate-permutable subgroup===
Conjugate-permutable subgroup ... ...
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title = Conjugate-permutable subgroups|
author = Tuval Foguel| ... paper defines the notion of conjugate-permutable subgroup, and proves ... ...
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If H is a conjugate-permutable subgroup of a group G, and S is any ... is also a conjugate-permutable subgroup of G.
==Related facts== ... ...
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The subgroup property of being a 2-subnormal subgroup is not stronger ... A 2-subnormal subgroup (a subgroup that is normal in a normal subgroup ... ...
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Any conjugate-permutable subgroup of a group is also conjugate-permutable ... If H is a conjugate-permutable subgroup of a group G, and H \le K ... ...
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is maximal among the proper fact about::permutable subgroups of G. Then, H ... * Maximal conjugate-permutable implies normal
* Pronormal implies self ... ...
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if every defining ingredient::conjugate-permutable subgroup of the subgroup ... * Stronger than::Conjugate-permutable subgroup
==Metaproperties== ... ...
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The concept and term were introduced in the paper Groups with conjugate ... A group is termed a C1-group if every cyclic subgroup is self-conjugate ... ...
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article Groups with all Cyclic subgroups Conjugate - Permutable which appeared ... A group is termed a CCP-group or a cyclic subgroups are conjugate ... ...
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final = conjugate-permutable subgroup}}
==Statement==
===Property-theoretic ... Automorph-permutable * Normal \le Normal
here * denotes the composition ... ...
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A subgroup of a group is termed a permutable 2-subnormal subgroup ... * Stronger than::Conjugate-permutable subgroup ... ...
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#redirect Self-conjugate-permutable subgroup ... ...
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quot; in a table means that the given subgroup property is invariant under ... ! Subgroup property !! Left transiter !! Right transiter !! Subordination ... ...
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weaker = self-conjugate-permutable subgroup}}
==Statement== ... The subgroup property of being pronormal is stronger than the subgroup ... ...
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A subgroup relation is a property that can be evaluated for an ordered ... * Conjugate-permutable subgroup: Conjugate \implies Permuting ... ...
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