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Officers received reports about the 31-year-old on Thursday, February 27, at around 2pm.
During a police search of the man, they allegedly found the weapon and also found him to be reportedly wanted for two other incidents.
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He was subsequently arrested and detained to appear in court for the alleged offences.
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Police Scotland Lanarkshire said: “About 2pm on Thursday February 27 2025 police received various reports of an intoxicated male walking on the Road in Cambuslang.
“Police located a 31 year old male matching the description. A search was carried out on the male before he was put into the police car and he was found to be in possession of a knuckleduster.
“The male was also wanted for 2 separate incidents. He was arrested and held to appear at court for the alleged offences.”