When Joseph Smith was killed, several men claimed to be his rightful successor. As a result, the Mormons fractured into many groups, all claiming to be the one true church. The largest splinter was the group who followed Brigham Young to Utah.
One group, believing that Joseph’s son should succeed him, moved to Independence MO and called themselves (as if the name was not long enough already) The Reorganized Church of Jesus Christ of Latter-Day Saints.
Heavily influenced by Smith’s 1st wife, Emma, who allied herself with this group, they rejected polygamy, denying that Joseph Smith was ever plurally married. Joseph’s son eventually uncovered the truth of his father’s sexual exploits. They reject many of the later revelations claimed by Smith, and reject the notion of multiple gods. They retained belief in the Book of Mormon and Joseph Smith as a true prophet. In fact, the beliefs of this group is much closer to the gospel taught in the Book of Mormon than is the Salt Lake church that followed Brigham Young.
They recently changed their name to The Community of Christ.
They also recently made belief in the historicity of the Book of Mormon optional (not a condition of membership in good standing). I am of the opinion that the Salt Lake church will eventually have to make the same concession.
Paul