Perhaps Sigmund Freud's most celebrated theory of sexuality, the Oedipus complex takes its name from the title character of the Greek play Oedipus Rex. In the story, Oedipus is prophesied to murder his father and have sex with his mother (and he does, though unwittingly). Freud argued that these repressed desires are present in most young boys. (The female version is called the Electra complex.)
D.H. Lawrence was aware of Freud's theory, and Sons and Lovers famously uses the Oedipus complex as its base for exploring Paul's relationship with his mother. Paul is hopelessly devoted to his mother, and that love often borders on romantic desire. Lawrence writes many scenes between the two that go beyond the bounds of conventional mother-son love. Completing the Oedipal equation, Paul murderously hates his father and often fantasizes about his death.
Paul assuages his guilty, incestuous feelings by transferring them elsewhere, and the greatest receivers are Miriam and Clara (note that transference is another Freudian term). However, Paul cannot love either woman nearly as much as he does his mother, though he does not always realize that this is an impediment to his romantic life. The older, independent Clara, especially, is a failed maternal substitute for Paul. In this setup, Baxter Dawes can be seen as an imposing father figure; his savage beating of Paul, then, can be viewed as Paul's unconsciously desired punishment for his guilt. Paul's eagerness to befriend Dawes once he is ill (which makes him something like the murdered father) further reveals his guilt over the situation.
But Lawrence adds a twist to the Oedipus complex: Mrs. Morel is saddled with it as well. She desires both William and Paul in near-romantic ways, and she despises all their girlfriends. She, too, engages in transference, projecting her dissatisfaction with her marriage onto her smothering love for her sons. At the end of the novel, Paul takes a major step in releasing himself from his Oedipus complex. He intentionally overdoses his dying mother with morphia, an act that reduces her suffering but also subverts his Oedipal fate, since he does not kill his father, but his mother.