Timeline for Generalization of normal subgroup
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 25, 2019 at 13:30 | review | Close votes | |||
| Jun 28, 2019 at 16:29 | |||||
| Jun 25, 2019 at 8:34 | comment | added | Geoff Robinson | If $A,B$ are subgroups, then we always have $[A,B] \lhd \langle A,B \rangle, $ so the conclusion that the commutator is normal in the intersection for a "normal pair" does not seem very strong.Your subgroups are just mutually normalizing, as Dirk says, which is a situation often encountered and well-studied. | |
| Jun 25, 2019 at 8:16 | comment | added | YCor | As mentioned, it's the combination of two properties which each are easily formulated using standard group theory language. I guess that "normal pair" could be misleading (a normal thing usually means something invariant under conjugation). | |
| Jun 25, 2019 at 7:19 | comment | added | Dirk | If I'm not mistaken, your property is equivalent to $A \subseteq N_G(B)$ and $B \subseteq N_G(A)$, where $N_G(\cdot)$ denotes the normalizer. Maybe this is already discussed somewhere? | |
| Jun 25, 2019 at 6:55 | history | asked | pre-kidney | CC BY-SA 4.0 |