Maybe I'm biased with stereotypes (taken obviously from movies and TV live-action series) but, in most prisons, are the most fragile inmates beaten up by gangs?

Whitey Bulger death In this case, yes. Whitey Bulger was a criminal that, at 89 years old, was transferred from solitary confinement to a prison in WV with the general population. He was killed within 24 hours. I’m sure it didn’t take much muscle to kill a frail 89 year old man.

Not necessarily the most fragile; elderly inmates are usually left alone unless they are trying to control others or are marked for being stoolies. Bulger had been an FBI informant, and was on hit lists.

Younger, weaker inmates may get punked by more domineering inmates. And it isn’t “beaten up by gangs”, it is being preyed upon by stronger inmates.

The gangs usually fall along racial lines, with subgroups based on outside gang affiliations. The gangs are more for protection from other gangs; the gangs don’t prey on weaker inmates unless the weaker inmate crosses a line of behavior.

Bulger was killed because he was a snitch.

Well, isn’t that just how society works in general?

I’ve badly phrased the question: I extend them also to stronger guys.

I can’t answer regarding prison, but I can tell you what I experienced in jail, in regards to women.
Nobody specifically looks to beat up random people without specific reason.
Some inmates will “nudge” newbies to find out if they could be a threat, a connection, a lover, etc.
During the few days I was in, there was a rumor circulated that I was in for harming a child. Some were planning bad stuff for me. Guards learned of the talk, and set it straight, that I was upset because my mom used the system to jail me just long enough to get her hands on my son, and disappear with him.
After that I was viewed with pity, for a while. Guards wanted to provide me an opportunity to escape, but I would not because that would put me on the run.
I garnered some respect from a young hooker was boasting she had high dollar regulars because she gave good head. I told her I’d never been paid, but I bet I was better. When she protested, I removed my upper denture. Her eyes got big, and she treated me to a cup of cocoa.
A lesbians made a move on me, even though I had made it known I went a different way. She got set straight in a private, but declarative way.
I huge woman who trended violent because she was only being given half the meds she was prescribed made an attempt to kill me. Several women restrained her and moved her to q rear cell until she could be medicated again, at which time she apologized.
I mentioned that I write poetry, and a line formed of women willing to pay two dollars each if I would tailor a poem for them to sent to someone. I partnered with a woman who did pastel artwork on pages to sell for stationary. She would do a page, give it to me to write a poem, and we would get two dollars each. One woman wanted me to write a poem for her husband who was also in jail. I quickly penned,
Roses are red
Violets are blue,
I’m in jail,
And so are you.
She loved the humor. I told her it was a joke, and she could use it for free, that I would write another. She chose to pay for both.
We did steady bartering like that, and it tended to set friendships, not to extend to the outside.
I got moved. The new batch of women also needed to check what I was about.
At dinner I went to an open spot and asked if the seat was taken. I just started eating and some chick nudged me and told me I was in her spot. I told her if anyone had objected before I sat down, I would have found another seat, but since nothing was said before I started to eat, I would be keeping my seat. Eyes got big, and she went somewhere else. I learned later she was considered the tough mama of the bunch. This was about fifty or sixty women.
Nothing came of it. She just checked me out, and learned I was not the back down type.
Soon after, they learned my favorite activity when we went to the yard was working with the punching bag.
I didn’t have anyone to hold it for me, so I just worked with the rhythm of the spins and returns. A few times women told me there were gloves available by request, to protect my knuckles. Hmph! I was pretending it was my mom. The blood dripping down my fingers felt like revenge. I told them it was not a problem. A guard told me also. I replied the same to her. A couple of days later a girl I spent time with talking a lot said somebody overheard the guards talking about me and one said they wouldn’t want to piss me off.
I had to laugh. I’m not the sort to go looking for a fight, but if one finds me I don’t walk away hurting.
So, in more detail than I intended to share, it is mostly a community which changes population rapidly, so almost every day someone is checking the pecking order. Only those with issues get involved with a ruckus, usually.

Never been to jail or prison, so I have no idea. Seems to happen in the movies a lot though.

I was in jail once. Just over night. Not fun. Food very nasty. Concrete floor, cold and hard. Impossible to sleep on. No pillow. One blanket. I was in there with 3 other women / girls who had been at a party together that got busted so they all knew each other. I just stayed in the corner by the toilet. There were guys in a cell next to us. Our metal toilet and their metal toilet were directly opposite and shared some plumbing. Sometimes the girls would take turns talking to one of the guys through the toilet. Since I was hunkered down by the toilet, it was on me to tell the girls if one of them got a toilet call. I didn’t know whether to laugh or cry.