Is it possible to use UCS core edition server in the company ?

I am writing an engineering thesis on Designing a server solution for a small/medium sized company based on Linux. And has a question if the core edition license can be used for free in the company. The purpose of the work is to show that you can find an alternative to windows server for free.

Sure you can: UCS is fully open source (our own code is mostly AGPLv3, but our base Debian distribution is a mix of many different licenses) and a subscription is optional.
There is just one gotcha: Our pre-build Debian packages (.deb) are actually under their own (proprietary) Core Edition Licence, which puts some restrictions on their use and hinders re-distribution. So strictly you would have to re-compile all packages yourself to be free of this limitation (but as UCS should builds reproducible you probably will get bit-identical packages anyway.)

There are some more “Subscription details”, e.g. some functions your’re not allowed to use without a subscription; see Prices and Subscriptions: The functions are always there and you can just use them, but by the Core Licence agreement you’re not allowed to use them. (Using them anyway will not trigger any notification and probably no-one from our side will care that you use it unless you become to big or are a million-euro-company.)