On the opposite side, I quit hiking with groups because in my efforts to keep up, I felt I was increasing my risk of an accident. I also prefer to be independent and set my own pace. I absolutely refuse to allow my children (who sometimes think they have become my parents) to dictate what I do. I had to make that very clear and hurt some feelings to accomplish this. However, I did compromise enough to buy a Personal Locator Beacon so I can "push the button" should I become seriously ill or injured (do remember, though, that it's only for life-and-death emergencies). I figure it's worth the extra 6 ounces to keep my kids off my back--a psychological weight saving! Of course by the time I got to that state, I'd been hiking/backpacking/horsepacking in the wilderness for over 50 years. If you're not experienced, my example is probably not a good idea.

If you can find a group that is mostly seniors, that might be your best bet. They should at least understand the needs of slower hikers.

Do you use trekking poles? I find that I can go quite a bit faster with them than without, and they greatly help with balance issues over rough ground. I use them even for exercise walking, because they turn walking into a whole-body exercise that works the core muscles.

EDIT, LATER: Hiking well-populated trails when lots of people are around is a reasonable substitute, safety-wise, for going with a group. You're independent, but there are people around to respond for a call for help. That's what I did when I first started hiking solo. I also made sure (from cars parked at the parking lot) that someone had gone up the trail ahead of me, and I started back early enough so that I wasn't the last person on the trail.