I was reading section 76 of the Doctrine and Covenants recently and a few questions occurred to me. I was always taught that the telestial kingdom is where all the bad people go, but that it's still a kingdom of glory and a pretty good place (just not as good as the others). I was also taught that those who go to outer darkness would be very few. Speculation abounded as to just what would be required to go there, and most people seemed to think that the only thing that would qualify is having a sure knowledge (like a personal visitation or something) of the Savior and then completely turning against that knowledge.
That definition was comforting on one hand, removing much of the fear of ever messing up so badly as to end up in eternal torment. On the other hand, it always sat wrong with me that basically that definition would mean that someone as totally evil as Hitler would end up with the same eternal fate as a liar or thief. I mean, yeah, they're both sinners, but there's a huge chasm in the magnitude of those sins.
As I was reading the definition of those in the telestial kingdom, I was struck by something. The people who go there are the unrepentant liars and adulterers, etc. Murderers aren't listed among those who inherit telestial glory. So, where do unrepentant murderers go?
From verses 31-38, we get a description of those who go to outer darkness:
31: Thus saith the Lord concerning all those who know my power, and have been made partakers thereof, and suffered themselves through the power of the devil to be overcome, and to deny the truth and defy my power—A few questions stood out to me:
32: They are they who are the sons of perdition, of whom I say that it had been better for them never to have been born;
33: For they are vessels of wrath, doomed to suffer the wrath of God, with the devil and his angels in eternity;
34: Concerning whom I have said there is no forgiveness in this world nor in the world to come—
35: Having denied the Holy Spirit after having received it, and having denied the Only Begotten Son of the Father, having crucified him unto themselves and put him to an open shame.
36: These are they who shall go away into the lake of fire and brimstone, with the devil and his angels—
37: And the only ones on whom the second death shall have any power;
38: Yea, verily, the only ones who shall not be redeemed in the due time of the Lord, after the sufferings of his wrath.
What does it mean to have been made a partaker of God's power?
What does it mean to have received the Holy Spirit? What does it mean to have denied the Holy Spirit?
What does it mean to have denied Christ?
What does it mean to have crucified Him unto oneself?
God's power is often equated with the priesthood in church discourse. Does that mean that only priesthood holders can go to outer darkness? I'm not sure that's a correct interpretation. In the temple, we are told that we're endowed with power from on high. So, I think those who have received the endowment who nonetheless have not been ordained to the priesthood are also partakers of God's power. Are there other ways to partake of God's power? I looked in the topical guide under the heading "God - Power of" to see what I could find. Most of the scriptures referred to resurrection. So, is anyone who will be resurrected (meaning anyone who ever lived on the earth) a partaker of God's power? That seems like a really broad definition, but it's possible.
When we are confirmed a member of the church, we're told to "receive the Holy Ghost". So, does confirmation trigger this element? I'm not convinced that it does. It is of note that the ordinance of confirmation does not confer the Holy Spirit on a person; the ordinance commands the person to receive the Holy Spirit. So, receiving the Holy Spirit is a personal event not mediated by priesthood ordinances. Someone who is not a member of the church could nonetheless receive the Holy Spirit, and someone who is a member of the church may not have.
Another interesting wrinkle in this question is how the interconnectedness of the Godhead plays into what it means to receive the Holy Spirit. The scriptures repeatedly affirm that the Father, Son, and Holy Spirit are one. So, receiving any member of the Godhead would count as receiving the Holy Spirit. Additionally, we find that whoever receives God's servants receives God. So, presumably, anyone who accepts any of the prophets (or other of God's servants) has received the Holy Spirit.
Since receiving any member of the Godhead counts as receiving any other member, presumably denying or rejecting any member of the Godhead counts as denying or rejecting any other. So, the element of denying the Holy Spirit and denying Christ is the same element. And how does one deny Christ? By crucifying Him unto oneself and putting Him to an open shame.
So, what does it mean to crucify Christ unto oneself? Crucifixion was the manner of His death. So, causing His death would qualify.  How does one cause the death of a being who has already died and been resurrected? Christ taught that whatever we do to others, it is as if we did it to Him.  So, murder would qualify as crucifying Christ unto oneself.
Putting this all together, it would appear that in at least some circumstances, an unrepentant murderer would qualify as a son or daughter of perdition. That said, I'm going to leave to God the judgment of the eternal fate of the souls of others.
 I'm avoiding the question for now as to whether murder is a forgivable sin upon sincere repentance. There appears to be authority on both sides of that question, so I'm focusing on the unrepentant in this post. I am also only focusing on murder, not on other forms of homicide, such as death caused by negligence or in self defense.
 While I support women's ordination to the priesthood, I don't think the endowment confers the priesthood on women.
 Doctrine and Covenants 84:36
 By this, I'm not referring to the fact that Christ died to pay for our sins. That was His choice, and while we should be eternally grateful, we didn't cause His death.
 See Matthew 25:34-46