Timeline for Product of Frattini Groups
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2017 at 23:01 | comment | added | YCor | The reference is: Dlab, Vlastimil ; Kořínek, Vladimír The Frattini subgroup of a direct product of groups. (English). Czechoslovak Mathematical Journal, vol. 10 (1960), issue 3, pp. 350-358, link dml.cz/handle/10338.dmlcz/100419 | |
| Oct 20, 2017 at 23:03 | comment | added | Russ Woodroofe | @YCor, thanks for clarifying dates. I edited slightly to reflect. Theorem 3 is certainly easier to apply than Theorem 1. | |
| Oct 20, 2017 at 22:52 | history | edited | Russ Woodroofe | CC BY-SA 3.0 |
clarified existence problem was unknown at the time of the paper
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| Oct 20, 2017 at 22:35 | comment | added | YCor | So of course it can look obsolete to state this equivalence since simple groups without maximal subgroups are now known to exist. But actually their Theorem 3 is more precise, and implies: let $\mathcal{C}$ be a class of groups stable under taking quotients, and in which every simple group has a maximal subgroup (examples: the class of finitely generated groups or the class of solvable groups); then $\Phi(G\times H)=\Phi(G)\times\Phi(H)$ for all $G,H\in\mathcal{C}$. | |
| Oct 20, 2017 at 22:27 | comment | added | YCor | Just to clarify the latter sentence: the linked paper is from 1960 and it was unknown at that time (at least to the authors) whether every simple group has a maximal subgroup. | |
| Oct 20, 2017 at 21:40 | history | answered | Russ Woodroofe | CC BY-SA 3.0 |