Timeline for Product-one sets in non-commutative groups
Current License: CC BY-SA 4.0
3 events
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| Jul 15, 2021 at 15:48 | comment | added | YCor | @TarasBanakh ($e$ neutral element) If there is a 2-cycle, say $a\mapsto b\mapsto a$, so $a=bc$, $b=ad$, for some $c,d\in D$. Hence $a=bc=adc$, so $dc=1$. If $d\neq c$, $dc=e$ contradicts $D$ being non-product-one. So $d=c$, and hence $c^2=e$, and this is excluded since you checked $D$ has no element of order $2$. | |
| Jul 4, 2021 at 14:41 | history | edited | YCor | CC BY-SA 4.0 |
simplified argument
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| Jul 4, 2021 at 9:26 | history | answered | YCor | CC BY-SA 4.0 |