Normal Subgroup of Group of Order 24/Mistake
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Source Work
1996: John F. Humphreys: A Course in Group Theory:
- Chapter $12$: Applications of Sylow Theory: $(6)$ Groups of order $24$:
- Proposition $12.7$
Mistake
- Thus $S_1$ and $S_2$ are both subgroups of $\map {N_G} T$, so $H = \gen {S_1, S_2}$ is a subgroup of $\map {N_T} G$ and hence $T$ is a normal subgroup of $H$.
Correction
The notation:
- $\map {N_G} T$
denotes the normalizer of $T$ in $G$: the largest subgroup of $G$ in which $T$ is a normal subgroup.
Hence the notation:
- $\map {N_T} G$
makes no sense in this context, and it should be another instance of $\map {N_G} T$.
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $12$: Applications of Sylow Theory: $(6)$ Groups of order $24$: Proposition $12.7$