Question: Let [itex]A[/itex] be a common subgroup of [itex]G[/itex] and [itex]H[/itex]. Show that if [itex]G \trianglelefteq (G \star_A H)[/itex] then [itex]G = A[/itex]. But before we go into this problem I'd like to ask a few, hopefully simple, questions. 1] What does the [itex]\trianglelefteq[/itex] symbol mean? Does it just mean that G is a normal subgroup of [itex]G \star_A H[/itex]? What is the difference between this and [itex]\triangleleft[/itex]? 2] So is this question basically asking prove that G = A if G is a normal subgroup of the free product amalgamated over A?