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inner_group_automorphism_group [2015/04/17 15:21] nikolaj |
inner_group_automorphism_group [2015/04/17 15:23] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $\langle\!\langle G,\cdot\rangle\!\rangle$ ... group | | | @#55CCEE: context | @#55CCEE: $\langle\!\langle G,\cdot\rangle\!\rangle$ ... group | | ||
| - | | @#FF9944: definition | @#FF9944: $\mathrm{Inn}(G)\equiv\langle\!\langle \{h\mapsto g\cdot h\cdot g^{-1}\},*\rangle\!\rangle$ | | + | | @#FF9944: definition | @#FF9944: $\mathrm{Inn}(G)\equiv\langle\!\langle \{h\mapsto g\cdot h\cdot g^{-1}\,\mid\,g\in G\},*\rangle\!\rangle$ | |
| | @#AAFFAA: inclusion | @#AAFFAA: $*$ ... pointwise function product w.r.t. $G$ and $\langle\!\langle G,\cdot\rangle\!\rangle$ | | | @#AAFFAA: inclusion | @#AAFFAA: $*$ ... pointwise function product w.r.t. $G$ and $\langle\!\langle G,\cdot\rangle\!\rangle$ | | ||
| ----- | ----- | ||
| === Elaboration === | === Elaboration === | ||
| + | Explicitly, pointwise function product means | ||
| + | |||
| $(\phi*\psi)(h):=\phi(h)\cdot\psi(h)$ | $(\phi*\psi)(h):=\phi(h)\cdot\psi(h)$ | ||
