Friend getting worse

We have a friend aged about 75, who lives alone and in the past. Every conversation is about how hard done by she was by mother/grandmother/ex-husband/daughter/everyone else on the planet and she makes shockingly nasty comments about everybody here in our small village, though never to their faces. She repeats herself constantly (even five minutes later) and gets very mixed up as her memory is obviously going south at speed. We used to invite her for lunch every sunday, but have now given up as we can't stand the nastiness. Recently she came round at 8pm saying she'd just come back from shopping (the last bus is at 6) and lost her keys and that the neighbours, who have a spare set, were out. We know that the neighbours were in and that they don't have a set in the first place. She eventually left at 9pm after we said that we were going to bed - quite truthfully. Now her downstairs neighbour tells me she has taken to sitting in the garden in her nightwear, talking to imaginary people and giving other invisibble people the royal wave. We are fairly sure that she suffers from Alzheimers or another affliction of the same variety. Despite the fact that she is so rude and unpleasant, we think something should be done, but have no idea what.

Does anybody have any advice? I could tell you many other instances of her current VERY strange behaviour, but that's enough for now.

Sorry this post is so long, but we are really rather worried.