You have faulty information. United Church of God, as an organization, was formed in 1995. Herbert Armstrong died in 1986. You're off by almost 10 years. You may want to do some research before posting:
See About UCG
Some of the more striking doctrines of the UCG are (1) rejection of the Trinity, (2) adoption of certain dietary laws and restrictions of the Hebrew Scriptures, (3) Saturday observance and (4) the particularly bizarre concept known as "British Israelitism."
The first three are certainly fundamental beliefs because they are beliefs that the 1st century church of Jesus Christ held.
"British Israelitism" is really a gross oversimplification of the belief that the leaders of the United States and Great Britain at one time believed the establishment of our countries were ordained and blessed by God. I think they were. As a result some of the prophecies and promises of the bible do extend to the present time and to our country. One of those prophecies is basically that we will go into captivity (economic or perhaps physical) because as a country we have turned on backs on the Lord Jesus Christ.
To better increase your understanding of the Lord and the early church you may wish to study some of these fundamental beliefs. Here's a good starting point:
The UCG is, I believe, currently split into two factions - the Luker group and the Kilough group.
Not even close. Dennis Luker has died and Clyde Kilough joined another group.
Thanks for the opportunity to set some of this straight!
The UCG was legally incorporated in 1995. But it didn't magically appear in 1995, it began as one of the factions in the WCG that were created by Armstrong's death.
The first three are certainly fundamental beliefs because they are beliefs that the 1st century church of Jesus Christ held.
The early Church upheld the Trinity (Matthew 28:19), the lack of necessity for festival observances (Colossians 2:16) and the abrogation of dietary laws (Acts 10:15).
"British Israelitism" is really a gross oversimplification of the belief that the leaders of the United States and Great Britain at one time believed the establishment of our countries were ordained and blessed by God.
That belief - which in itself is theologically questionable - is different from the principle of British Israelitism, which both the WCG and UCG supported/support. Armstrong's book The United States and Britain in Prophecy forms the core of this belief in the UCG and WCGA.
Dennis Luker has died
Are you arguing that once someone dies, his followers stop supporting his views? The UCG exists because of ongoing dedication to Armstrong's views after his demise.
and Clyde Kilough joined another group
Kilough did not join someone else's group - he split the UCG by founding the Church of God Worldwide Association, or CGWA. His view is that the UCG has been corrupted and that the CGWA upholds the original UCG teachings.
The UCG exists because its founders believe that it upholds the true WCG beliefs and that the current GCI has corrupted the old WCG.
All three groups derive their worldview from Herbert Armstrong, are all factions of Armstrong's organization, and all claim to be the original and authentic upholders of 1st century Christianity.
Armstrong himself split off from the CGSD.