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On the Schur Index of Quasi-Primitive Characters
Journal of the London Mathematical Society, 1987A way to calculate the Schur index of a quasi-primitive character of a finite group via factorizations of characters [see \textit{P. Ferguson} and \textit{A. Turull}, Math. Z. 190, 583-604 (1985; Zbl 0577.20006)] is given. It follows from it that, if the Schur indexes of the irreducible characters of the covering groups of the finite simple groups are ...
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On Bounding the Schur Index of Induced Modules
Bulletin of the London Mathematical Society, 1986The author proves the following result, which confirms a conjecture of the reviewer. Theorem. Let k be an algebraic number field and H be a subgroup of a finite group G. Let V be a kH-module such that the induced module \(V^ G\) is irreducible. Then the index of \(End_{kG}(V^ G)\) is bounded by a function of \(| H|\) alone.
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The Schur index and Moody's theorem
K-Theory, 1993The Schur index of a central simple algebra \(A\) over a field \(F\) is the degree of the division algebra which is Brauer-equivalent to \(A\). The purpose of this paper is to prove formulas describing how the Schur index of a central simple algebra is reduced when scalars are extended to the function field of certain varieties of ideals in central ...
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ON THE SCHUR INDEX OF PROJECTIVE REPRESENTATIONS OF FINITE GROUPS
Mathematics of the USSR-Sbornik, 1971This work is a study of the set of Schur indices of absolutely irreducible projective representations of nilpotent groups over a field which is a finite extension of the rational number field or of the rational -adic number field . Bibliography: 13 titles.
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About the Schur Index for Ambivalent Groups
Communications in Algebra, 2013An ambivalent group is a finite group all of whose irreducible characters are real valued. By Brauer–Speiser theorem, if G is an ambivalent group, then the absolute Schur index m Q (χ) = m(χ) ≤2. In this note we shall prove that this property is true also for the derived subgroups of ambivalent groups.
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Some Results on the Schur Index of a Representation of a Finite Group
Canadian Journal of Mathematics, 1970Let ℭ be a finite group with a representation as an irreducible group of linear transformations on a finite-dimensional complex vector space. Every choice of a basis for the space gives the representing transformations the form of a particular group of matrices.
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