The Collaborative International Dictionary of English v.0.48:

Alogian \A*lo"gi*an\, n. [LL. Alogiani, Alogii, fr. Gr. ?; 'a
   priv. + ? word.] (Eccl.)
   One of an ancient sect who rejected St. John's Gospel and the
   Apocalypse, which speak of Christ as the Logos. --Shipley.
   [1913 Webster]