Timeline for Are isomorphic quotients of abelian groups induced by automorphisms?
Current License: CC BY-SA 4.0
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| May 15, 2021 at 10:06 | comment | added | YCor | Actually, if the result were true, say for finite abelian groups, then it would follow that in an abelian group all subgroups of the same prime index are isomorphic, and by induction that all subgroups of the same cardinal are isomorphic. This is indeed false and $C_2\times C_4$ is the smallest counterexample (with non-isomorphic subgroups of order 4). | |
| May 15, 2021 at 9:50 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| May 15, 2021 at 9:45 | history | undeleted | Francesco Polizzi | ||
| May 15, 2021 at 9:45 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| May 15, 2021 at 9:35 | history | deleted | Francesco Polizzi | via Vote | |
| May 15, 2021 at 9:18 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| May 15, 2021 at 9:12 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| May 15, 2021 at 8:50 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| May 15, 2021 at 8:48 | comment | added | Wojowu | There is also an abelian counterexample, $G=\mathbb Z_4\times\mathbb Z_2$. | |
| May 15, 2021 at 8:43 | history | answered | Francesco Polizzi | CC BY-SA 4.0 |