A lot of shops will add Rift Lake water conditioner to their cichlid tanks to increase the GH (general hardness), KH (carbonate hardness) and pH of the water. I have to do the same in Perth WA because we have very soft water with virtually no minerals in. I used Aquasonic Rift Lake conditioner and add enough to raise the GH to around 300ppm for Lake Malawi cichlids and 400ppm for Lake Tanganyikan cichlids. The peacock cichlids (Aulonocara sp) you have are from Lake Malawi.
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The peacock cichlids you have look like males and the dominant one will bully weaker males. You can reduce aggression by having lots of hiding places and by getting juvenile fish and letting them grow up together. Unfortunately, by putting a group of adult males together, they will probably argue over territories and the biggest one usually wins.
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If you visit a pet shop, ask them if they add anything to raise the pH, GH and KH of their water for their Rift Lake cichlids.
You might also want to find another pet shop if your current one sells you any fish without asking about tank conditions (water chemistry, how long it's been set up for, how big the tank is, etc). Good shops will usually ask these questions before catching out any fish for you. It gives them an idea about what you can and can't stock in the tank and they can direct you towards fishes that are more suited to the tank and water you have.
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If you want to keep the cichlids you currently have, minimise feeding for a few weeks.
Monitor ammonia, nitrite, nitrate and pH levels until you are sure the filters have established.
Add some limestone rocks, flower pots or ornaments with holes in to make hiding places.
Add some Rift lake conditioner. You will need to add this to any new water before it goes in the tank. You need to make the water up 24 hours before using it so all the mineral salts dissolve completely.