The Schur multiplier, fields, roots of unity, and a natural splitting
نویسندگان
چکیده
منابع مشابه
Computing Roots of Unity in Fields
The paper is in four sections. First we provide some necessary background to computing in fields; then follows a collection of algebraic lemmas. In Section 3 we prove the theorem and in Section 4 append useful information on related decision problems. These theorems are straightforward contributions to Computable Algebra, to work on fields and (non finitely presented) groups (see Sections 1 and...
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On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group
Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement...
متن کاملVANISHING SUMS OF mTH ROOTS OF UNITY IN FINITE FIELDS
In an earlier work, the authors have determined all possible weights n for which there exists a vanishing sum ζ1 + · · · + ζn = 0 of m th roots of unity ζi in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic p. For given m and p, results are obtained on integers n0 such that all integers n ≥ n0 are in the “weight set” Wp(m). The main result (1.3) i...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1990
ISSN: 0021-8693
DOI: 10.1016/0021-8693(90)90231-c