One God:
Alma 11:27-39, 44
27 And Amulek said: Yea, there is a true and living God.
28 Now Zeezrom said: Is there more than one God?
29 And he answered, No.
30 Now Zeezrom said unto him again: How knowest thou these things?
31 And he said: An angel hath made them known unto me.
32 And Zeezrom said again: Who is he that shall come? Is it the Son of God?
33 And he said unto him, Yea.
34 And Zeezrom said again: Shall he save his people in their sins? And Amulek answered and said unto him: I say unto you he shall not, for it is impossible for him to deny his word.
35 Now Zeezrom said unto the people: See that ye remember these things; for he said there is but one God; yet he saith that the Son of God shall come, but he shall not save his people—as though he had authority to command God.
36 Now Amulek saith again unto him: Behold thou hast lied, for thou sayest that I spake as though I had authority to command God because I said he shall not save his people in their sins.
37 And I say unto you again that he cannot save them in their sins; for I cannot deny his word, and he hath said that no unclean thing can inherit the kingdom of heaven; therefore, how can ye be saved, except ye inherit the kingdom of heaven? Therefore, ye cannot be saved in your sins.
38 Now Zeezrom saith again unto him: Is the Son of God the very Eternal Father?
39 And Amulek said unto him: Yea, he is the very Eternal Father of heaven and of earth, and all things which in them are; he is the beginning and the end, the first and the last;
44 Now, this restoration shall come to all, both old and young, both bond and free, both male and female, both the wicked and the righteous; and even there shall not so much as a hair of their heads be lost; but every thing shall be restored to its perfect frame, as it is now, or in the body, and shall be brought and be arraigned before the bar of Christ the Son, and God the Father, and the Holy Spirit, which is one Eternal God, to be judged according to their works, whether they be good or whether they be evil.
2 Nephi 31:21
21 And now, behold, my beloved brethren, this is the way; and there is none other way nor name given under heaven whereby man can be saved in the kingdom of God. And now, behold, this is the doctrine of Christ, and the only and true doctrine of the Father, and of the Son, and of the Holy Ghost, which is one God, without end. Amen.
Mosiah 15:1-5
1 And now Abinadi said unto them: I would that ye should understand that God himself shall come down among the children of men, and shall redeem his people.
2 And because he dwelleth in flesh he shall be called the Son of God, and having subjected the flesh to the will of the Father, being the Father and the Son—
3 The Father, because he was conceived by the power of God; and the Son, because of the flesh; thus becoming the Father and Son—
4 And they are one God, yea, the very Eternal Father of heaven and of earth.
5 And thus the flesh becoming subject to the Spirit, or the Son to the Father, being one God, suffereth temptation, and yieldeth not to the temptation, but suffereth himself to be mocked, and scourged, and cast out, and disowned by his people.
3 Nephi 11:27
27 And after this manner shall ye baptize in my name; for behold, verily I say unto you, that the Father, and the Son, and the Holy Ghost are one; and I am in the Father, and the Father in me, and the Father and I are one.
Mormon 7:7
7 And he hath brought to pass the redemption of the world, whereby he that is found guiltless before him at the judgment day hath it given unto him to dwell in the presence of God in his kingdom, to sing ceaseless praises with the choirs above, unto the Father, and unto the Son, and unto the Holy Ghost, which are one God, in a state of happiness which hath no end.
Analysis
While the Book of Mormon claims that the Father, the Son, and the Holy Ghost are one God, the definition give is more in line with the heretical doctrine of Modalistic Monarchianism (accepted as true by United Pentecostals today) than it is with the Trinity. According to modalism, the three names for God refer to the three “modes” by which God reveals himself.
https://www.mrm.org/trinity-book-of-mormon