I have tried several things but it doesn't work.
It seems that the Broadcom BCM43142 has some problems with the Ubuntu 16.04 base kernel that elementary OS Loki uses. There are two solutions for this.
Option 1. Install the Kernel built specifically for your Wi-Fi Module
Run the following two commands in the terminal:
sudo apt update sudo apt install bcmwl-kernel-source
Option 2. Blacklist the offending items manually.
Edit the blacklist file with this command:
sudo nano /etc/modprobe.d/blacklist.conf
Then append the following lines:
blacklist b43 blacklist bcma blacklist ssb