Beets do not fix nitrogen, but the small root hairs can become infected by soil-dwelling bacteria, which cause small tumors to form. These bacteria are present in many soils, and they are closely related to the rhizobia that help legumes fix nitrogen. In a way, those nitrogen nodules on legume roots are tumors, too, only the plants have figured out a way to make use of them. So far, we know of no benefit to seeing little tumors on beets, carrots, and a few other crops. Rub them off and enjoy your beets!

Here is a link that might be useful: my website

Very interesting... Thanks.
Is it likely that these "tumors" are going to show up on anything that I plant in that planter? Does the "tumors" affect the growth of other plants such as melons, squash or gourds?

I think the only vegetable/herb that's seriously bothered is carrots, but grapes, fruit and nut trees can be affected by Agrobacterium tumefaciens. I have it in my garden, and some carrots will be fine while others will have lots of knobs and tumors. I've never seen it on other root crops, so I think it takes a convergence of soil temp, moisture, and host plant that get it active.

Interestingly, the "signaling" magic the bacteria uses to interfere with plants' DNA in order to make them form cozy tumors is much admired in microbiology circles.

Here is a link that might be useful: my website

Or the roots may be affected by root knot nematode.

Can you post a photo?

Too late for photos: As I took the time to look closely at the small Beet crop, I noted 2 things.
1. nearly all of the plants had the knots and
2. only about 1/3 of the crop had beets large enough to be worth the effort to continue. They had been in the ground longer that the harvest time indicated on the seed pack.
So I decided to just pull them all, set what I could to pickle and plant something else in the planter.
As the planter is on the front porch (all of my plantings have to be in a container of some sort due to space considerations) and not very large at that, I put a couple of cabbage seeds at one end of it and a couple of bib lettuce at the other end.