I'll continue looking, but if you could point me to this law I'd really appreciate it. In any case, If I did ever carry it, it would be open carry with the selector switch set to single shot.
I did a search of the Utah State law repository at
http://le.utah.gov and only found a definition of a "fully automatic weapon" and a penalty for transferring a fully automatic weapon to a minor, so I have over stated. It would seem to be legal with a concealed carry permit to CONCEAL a fully automatic firearm BUT NOT a SBR or SBS!
http://le.utah.gov/~code/TITLE76/htm/76_10_050904.htm
76-10-509.4. Prohibition of possession of certain weapons by minors.
(1) A minor under 18 years of age may not possess a handgun.
(2) Except as provided by federal law, a minor under 18 years of age may not possess the following:
(a) a sawed-off rifle or sawed-off shotgun; or
(b) a fully automatic weapon.
(3) Any person who violates Subsection (1) is guilty of:
(a) a class B misdemeanor upon the first offense; and
(b) a class A misdemeanor for each subsequent offense.
(4) Any person who violates Subsection (2) is guilty of a third degree felony.
Amended by Chapter 80, 1995 General Session
and
http://le.utah.gov/UtahCode/getCodeSection?code=76-10-509.5
76-10-509.5. Penalties for providing certain weapons to a minor.
(1) Any person who provides a handgun to a minor when the possession of the handgun by the minor is a violation of Section 76-10-509.4 is guilty of:
(a) a class B misdemeanor upon the first offense; and
(b) a class A misdemeanor for each subsequent offense.
(2) Any person who transfers in violation of applicable state or federal law a sawed-off rifle, sawed-off shotgun, or fully automatic weapon to a minor is guilty of a third degree felony.
Amended by Chapter 94, 1994 General Session
Here is what I found related to concealment of short barrelled rifles or short barrelled shotguns, NOT FULLY AUTOMATIC FIREARMS . See (3) below.
http://le.utah.gov/~code/TITLE76/htm/76_10_050400.htm
76-10-504. Carrying concealed dangerous weapon -- Penalties.
(1) Except as provided in Section 76-10-503 and in Subsections (2), (3), and (4), a person who carries a concealed dangerous weapon, as defined in Section 76-10-501, including an unloaded firearm on his or her person or one that is readily accessible for immediate use which is not securely encased, as defined in this part, in or on a place other than the person's residence, property, a vehicle in the person's lawful possession, or a vehicle, with the consent of the individual who is lawfully in possession of the vehicle, or business under the person's control is guilty of a class B misdemeanor.
(2) A person who carries a concealed dangerous weapon which is a loaded firearm in violation of Subsection (1) is guilty of a class A misdemeanor.
(3) A person who carries concealed a sawed-off shotgun or a sawed-off rifle is guilty of a second degree felony.
(4) If the concealed firearm is used in the commission of a violent felony as defined in Section 76-3-203.5, and the person is a party to the offense, the person is guilty of a second degree felony.
(5) Nothing in Subsection (1) or (2) shall prohibit a person engaged in the lawful taking of protected or unprotected wildlife as defined in Title 23, Wildlife Resources Code of Utah, from carrying a concealed weapon or a concealed firearm with a barrel length of four inches or greater as long as the taking of wildlife does not occur:
(a) within the limits of a municipality in violation of that municipality's ordinances; or
(b) upon the highways of the state as defined in Section 41-6a-102.
Amended by Chapter 362, 2009 General Session