I am looking for some examples of odd order finite groups, that are not isomorphic to the group of units of some ring (ring has identity and is associative)
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See also https://math.stackexchange.com/questions/384422/which-finite-groups-are-the-group-of-units-of-some-ring – lhf Jun 03 '21 at 14:16
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@lhf Thank you for your reply. I saw this post. Answers there focus on classifying groups, that are unit groups of ring. I tried to think of some solutions for my question, based on that classification, but failed and decided to ask here – personalfebus Jun 03 '21 at 14:31
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I think $C_5$ is an example. See https://math.stackexchange.com/questions/73498/is-the-group-of-units-of-a-finite-ring-cyclic – lhf Jun 03 '21 at 15:44
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@lhf Could you provide some proof on why C5 satisfies the conditions. Also answer, that you linked addresses only commutative rings or maybe i missed something – personalfebus Jun 03 '21 at 19:58
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1See https://math.stackexchange.com/questions/384362/group-of-invertible-elements-of-a-ring-has-never-order-5 – lhf Jun 05 '21 at 12:55
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@lhf Thank you! – personalfebus Jun 05 '21 at 19:46