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The Collaborative International Dictionary of English v.0.48:

Abelian \A*bel"i*an\, Abelite \A"bel*ite\, Abelonian \A`bel*o"ni*an\, n. (Eccl. Hist.) One of a sect in Africa (4th century), mentioned by St. Augustine, who states that they married, but lived in continence, after the manner, as they pretended, of Abel. [1913 Webster]