# projective unitary groups in a sentence

- Pierre Deligne and George Mostow used his ideas to construct lattices in the
*projective unitary group*. - This omitted certain known groups ( the
*projective unitary groups*), which were obtained by " twisting " the Chevalley construction. - O'Nan received his PhD in 1970 from Princeton University under Daniel Gorenstein with thesis " A Characterization of the Three-Dimensional
*Projective Unitary Group*over a Finite Field ". - In this case the central extended group corresponding to the first projective representation of each
*projective unitary group*is just the original unitary group of which we took the quotient by U ( 1 ) in the definition of PU. - The quotient of the unitary group by its center is called the "'
*projective unitary group*"',, and the quotient of the special unitary group by its center is the "'projective special unitary group " '. - It's difficult to find
*projective unitary groups*in a sentence. - 蒻ile Picard sought to extend the work of Schwarz in complex geometry, by means of a generalized hypergeometric function, to construct cases of equations where the monodromy was a discrete group in the
*projective unitary group*" PU " ( 1, " n " ). - The above is for the classical unitary group ( over the complex numbers ) for unitary groups over finite fields, one similarly obtains special unitary and
*projective unitary groups*, but in general \ operatorname { PSU } ( n, q ^ 2 ) \ neq \ operatorname { PU } ( n, q ^ 2 ). - The complex projective orthogonal group, PO ( " n ", "'C "') should not be confused with the
*projective unitary group*, PU ( " n " ) : PO preserves a symmetric form, while PU preserves a hermitian form PU is the symmetries of complex projective space ( preserving the Fubini Study metric ). - This construction is important in the study of the sporadic groups, and in much of the exceptional behavior of small classical and exceptional groups, including : construction of the Mathieu group M 24, the exceptional covers of the
*projective unitary group*U _ 4 ( 3 ) and the projective special linear group L _ 3 ( 4 ), and the exceptional double cover of the group of Lie type G _ 2 ( 4 ).

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