Reboot after login

Last week I tried to install Ubuntu Mate 20.04 daily on Acer Aspire One D270 (Intel Atom N2600 1.6 Ghz CPU, with 2 GB of RAM and 128 GB SSD). The installation was completed but when I restarted the computer, after logging in, the system rebooted automatically, without any intervention on my part. I tried to download a new version of Ubuntu Mate a few days later, I prepared the USB stick with Balena Etcher and I redid the installation from scratch, but the result is always the same. I thought it could possibly depend on some configuration file left in the old home directory (which I had not formatted), so I backed up all the data, formatted the PC and installed it from scratch. Arrived at the login, always the same situation. I had to install Ubuntu Mate 18.04 again because I can't start Ubuntu Mate 20.04 correctly.

Hello Carlo, welcome:
Is your laptop model ACER Aspire One 32bit?
In that considering, is your Ubuntu iso 'ubuntu-mate-18.04.4-desktop-i386'? Bionic (18.04) is last version in that architecture, so 20.04 is no already longer available.

Lucky

No, my laptop is 64 bit... Now I have 18.04 64 bit on it

32/64 bit... yes...but a bit limited perhaps for 20.04. Of course the processor is 64 (I think it was made for windows 7 starter 32bit, though is possible W7 64bit ), but RAM is only 2Gb. I'm not saying the problem it's there but...
Carlo, I have also an Aspire One 255 1Gb an I LOVE it, hard like a Rock!! But actually only use it for graphic card and VGA connector...