2
votes
Accepted
Inverse bijections between subgroups of $G$ containing the kernel and subgroups of $H$ contained in the image.
It isn't true that $(\varphi^{-1} \circ \varphi)(A)=A$.
Suppose $G = \mathbb{Z},\ A = \{0\},\ H = \{0\}$ and $\varphi(n) = 0\quad \forall n \in \mathbb{Z}$
then $(\varphi^{-1} \circ \varphi)(A) = G \...
- 140
1
vote
Accepted
Proving equivalence of two definitions of "field"
I'm going to try to clarify your question before i give the answer to my interpretation of it...
A field (F,+,x) is often either defined using 9 axioms or by simply saying:
$(F,+)$ and $(F\setminus\{...
- 100
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