[long]
Joseph Cook has given a partial answer, but it is perhaps worth explaining the setup again, as we do periodically.
First, though you are reading the messages using Google Groups, soc.genealogy.medieval is not a Google Group, it is a Usenet group. As Joseph explained, this is a distributed messaging network, where individual internet service providers have a Usenet server with a set of folders for the Usenet groups, and these folders contain the messages. Any time a participant posts a message, it goes into their ISP's folder for that group. The ISP's server regularly contacts other Usenet servers, and when they do, they compare each group folder, and exchange any new messages. In this way, messages spread like a virus through peer-to-peer contacts. A Usenet group could be set up either as moderated or non-moderated, but at the time the group was set up, there was an extremely high bar to establish moderated groups that discussions of medieval genealogy never could have met, so it was established as an unmoderated group, with no administrator.
Back in the day, this is primarily how the group was followed. However, for over 20 years, there was an alternative interface - RootsWeb set up a system to harvest all of the messages from the Usenet group soc.genealogy.medieval and deposit them on a mailing list, called GEN-MEDIEVAL, which served as a mirror for soc.gen.med. This enabled someone to either receive every message in their inbox, or to receive a daily digest so they could then go check the archive for the relevant posts of interest. It also allowed responses by mail that were converted into Usenet messages and placed in their group folder, to enter the Usenet stream. To make a long story short, RootsWeb sold out to Ancestry who ran business as usual but with practically non-existent support, but then after years of operating it they changed their server configuration, broke the connection with Usenet, and outright lied by saying that there had never had any linkage. This severed soc.gen.med from GEN-MED, which became moribund, and then they shut down their mailing lists entirely, so this alternative interface no longer exists.
Another alternative interface was operated by a system called Deja News (later Deja.com), which offered a web-based interface for Usenet groups, and more importantly, maintained an archive. Analogous arrangement as with GEN-MEDIEVAL. They harvested the messages from Usenet and presented them on a web page format. They got bought out by Google, who decided to functionally integrate the Usenet web interface into their Google Groups message boards. They have a server that does the standard Usenet peer-to-peer message sharing, but this harvests messages and converts them into the format of message board posts, and likewise converts responses on the Message board into Usenet messages to be injected into the Usenet flow. Google being Google, they have to pretend that none of the back end is happening, that it is an entirely Google-contained experience, that you are looking at a Google Group named soc.genealogy.medieval, rather than just a web interface for Usenet group of that name. They don't tell you it is Usenet, and they don't tell you there is no administrator (which they have for their real Google Groups but is meaningless in the context of an unmoderated Usenet group). Call me skeptical, but I suspect it is only a matter of time before they follow Ancestry's precedent, cut the link to Usenet and pretend it was never there, but for now the messages you are seeing on Google Groups have come either through direct posting to Google Groups or through the Usenet interface with the 'real' soc.gen.med group, with no administrative involvement.
Is there a specific question you have? There is no administrator to answer it, but there are long-term participants who may be able to answer some questions.
taf