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The phrase "established a group" is correct and usable in written English.
You can use it when you want to describe creating a new group of people or things. For example: "John established a group of volunteers to help clean up the local park."
Exact(34)
The Union itself — as befits Brussels' bureaucracy — has established a group to deal with these issues and is cooperating with the Council of Europe's Group of States against Corruption.
He and a friend Sébastien Foucan established a group of traceurs called the Yamakasi.
He also established a group in Sierra Leone for the emigration of free blacks who wanted to escape racial problems.
Last May, the canton established a group to study the options, promising a report by the end of last year.
Jenny Jarvis, a researcher at the University of Nairobi, established a group in her lab, but could not understand why so few of them seemed to breed.
He established a group page on Facebook, so that former members of Fox Company could recall the details of the day.
Similar(25)
Maizels et al. [15] established a group-based model of disease management for patients with headache.
The GDH and GSIS established a group-based secret key and a group-based public key individually.
Once established a grouping pattern, one should not break it.
Fast Society's ability to establish a group's expiration date is a major advantage.
Mr. Friedman began his organizing career by establishing a group to lobby against car alarms.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com