What is that braid like thing around the shoulder of a US army officer's uniform, and why do only men have it?

It's over the shoulder and it's braided I've seen it come in blue or white and it's usually on the right or left shoulder and I noticed only the men have it on their uniforms, females do not, how come? Also Major Zod from Smallville wore that braid like thing on his Kryptonian officer uniform. What... show more It's over the shoulder and it's braided I've seen it come in blue or white and it's usually on the right or left shoulder and I noticed only the men have it on their uniforms, females do not, how come? Also Major Zod from Smallville wore that braid like thing on his Kryptonian officer uniform. What does the braid like thing symbolize, and also what did the purple patch on Major Zod's uniform symbolize?
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