On Maximal Chains In Partially Ordered Sets With Compatible (Left, Right)- Group Actions

In this paper, we deal with compatible (left, right)-group actions on posets, i.e; (G, H)-posets. Our main purpose in this work is to study the maximal chains in (G, H)-posets to observe that this study gives us indications on the type of some (G, H) actions on posets. Therefore, we shall study the behavior of the (G, H) actions on chains.