My massage therapist gave me a book entitled Manual of Structural Kinesiology that shows where muscles attach and what they do. Since muscles have two ends, every muscle can move either end or both at the same time so that it is not always clear cut what a particular muscle can do. Also, muscles can function in combinations with other muscles which also clouds their function. For example, a hanging raise will involve the psoas group will raise the thigh but since the upper attachment point is to the vertibra, the movement will tip the pelvis and this tipping itself is prevented by the abdominals. If abs are not strong enough or have enough endurance, say toward the end of a long ride, back pain is a possibility. https://en.wikipedia.org/wiki/Psoas_major_muscle

There are a number of muscle groups that attach to the pelvis and are responsible for many different types of movement. Maintaining a strong core is good for cycling but also for many other types of movement including getting groceries into the house.