Does kafka group works independent of kafka topic?

I have a situation as – I have two java application(lets say a1 and a2) running with same kafka consumer group(lets say g1) and on different topics(lets say t1 and t2) and have only 1 partition(lets say p1). a1 consume messages from t1 and produces to t2. a2 consume messages from t2 and do some processing. In such situation, Could a1 hold or create blockage for a2 so that a1 remains idle and not doing anything or not consuming any messages? I am getting messages consumed by a2 when using different group but with same group g1, no luck at all.