Abstract

Let [Formula: see text] be a group. Two elements [Formula: see text] are said to be in the same [Formula: see text]-class if their centralizers in [Formula: see text] are conjugate within [Formula: see text]. In this paper, we prove that the number of [Formula: see text]-classes in the group of upper triangular matrices is infinite provided that the field is infinite and size of the matrices is at least [Formula: see text], and finite otherwise.

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