Kant states his third formulation of the categorical imperative on page 44. On page 45, he attaches the concept of a "kingdom of ends" to this formulation.
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Kant's third formulation of the categorical imperative is often referred to as the "formula of autonomy." It states that one should always act in such a way that the maxim of their action can become a universal law for all rational beings. In other words, individuals should act in a way that treats others as ends in themselves, rather than means to an end.
On page 45, Kant introduces the concept of a "kingdom of ends" in relation to the third formulation. He argues that when individuals act in accordance with the categorical imperative, they are essentially participating in a moral community where all rational beings are treated as ends. This "kingdom of ends" is not a physical kingdom but a hypothetical realm in which everyone respects each other's inherent worth and dignity.
In this conceptual "kingdom," individuals recognize the equal moral worth of all rational beings and interact with each other based on that principle. Thus, the notion of a "kingdom of ends" is an important idea in Kantian ethics, highlighting the ideal moral community where people are treated with respect and dignity, and moral principles are universally applied.