Nilpotent Hall implies isomorph-conjugate
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a finite group. That is, it states that in a Finite group (?), every subgroup satisfying the first subgroup property (i.e., Nilpotent Hall subgroup (?)) must also satisfy the second subgroup property (i.e., Isomorph-conjugate subgroup (?)). In other words, every nilpotent Hall subgroup of finite group is a isomorph-conjugate subgroup of finite group.
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- Nilpotent Hall subgroups of same order are conjugate
- Sylow implies intermediately isomorph-conjugate
- Hall implies join of Sylow subgroups
- Nilpotent join of intermediately isomorph-conjugate subgroups is intermediately isomorph-conjugate
- Hall not implies isomorph-conjugate
- Hall not implies isomorph-automorphic
- Nilpotent Hall not implies order-conjugate
Proof using fact (1)
The proof follows directly from fact (1).
Proof using facts (2)-(4)
The proof follows directly by combining facts (2)-(4).