1,721,052 research outputs found
The orders of nonsingular derivations of modular Lie algebras
No full textWe extend the results of Shalev [Sh] on the orders of nonsingular derivations of finite-dimensional non-nilpotent modular Lie algebras.The author is grateful to Ministero dell’Università e della Ricerca Scientifica, Italy, for financial support to the project “Graded Lie algebras and pro-p-groups of finite width”.</p
The orders of nonsingular derivations of modular Lie algebras
No full textWe extend the results of Shalev [Sh] on the orders of nonsingular derivations of finite-dimensional non-nilpotent modular Lie algebras.The author is grateful to Ministero dell’Università e della Ricerca Scientifica, Italy, for financial support to the project “Graded Lie algebras and pro-p-groups of finite width”.</p
A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra
No full textA study of the set N_p of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p>0 was initiated by Shalev and continued by the present author. The main goal of this paper is to produce more elements of N_p. Our main result shows that any divisor n of q ? 1, where q is a power of p, such that n ? (p ? 1)^{1/p} (q ? 1)^{1?1/(2p)}, necessarily belongs to N_p. This extends its special case for p = 2 which was proved in a previous paper by a different method.</p
A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra
No full textA study of the set N_p of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p>0 was initiated by Shalev and continued by the present author. The main goal of this paper is to produce more elements of N_p. Our main result shows that any divisor n of q ? 1, where q is a power of p, such that n ? (p ? 1)^{1/p} (q ? 1)^{1?1/(2p)}, necessarily belongs to N_p. This extends its special case for p = 2 which was proved in a previous paper by a different method.</p
The orders of nonsingular derivations of Lie algebras of characteristic two
No full textNonsingular derivations of modular Lie algebras which have finite multiplicative order play a role in the coclass theory for pro-p groups and Lie algebras. A study of the set NpNp of positive integers which occur as orders of nonsingular derivations of finite-dimensional nonnilpotent Lie algebras of characteristic p > 0 was initiated by Shalev and continued by the present author. In this paper we continue this study in the case of characteristic two. Among other results, we prove that any divisor n of 2k ? 1 with n4 > (2k ? n)3 belongs to N2N2 . Our methods consist of elementary arguments with polynomials over finite fields and a little character theory of finite groups.This work was partially supported by Ministero dell’Istruzione e dell’Università, Italy, through PRIN “Graded Lie algebras and pro-p-groups of finite width”.</p
The orders of nonsingular derivations of Lie algebras of characteristic two
No full textNonsingular derivations of modular Lie algebras which have finite multiplicative order play a role in the coclass theory for pro-p groups and Lie algebras. A study of the set NpNp of positive integers which occur as orders of nonsingular derivations of finite-dimensional nonnilpotent Lie algebras of characteristic p > 0 was initiated by Shalev and continued by the present author. In this paper we continue this study in the case of characteristic two. Among other results, we prove that any divisor n of 2k ? 1 with n4 > (2k ? n)3 belongs to N2N2 . Our methods consist of elementary arguments with polynomials over finite fields and a little character theory of finite groups.This work was partially supported by Ministero dell’Istruzione e dell’Università, Italy, through PRIN “Graded Lie algebras and pro-p-groups of finite width”.</p
Inversion and subspaces of a finite field
No full textConsider two F q -subspaces A and B of a finite field, of the same size, and let A ?1 denote the set of inverses of the nonzero elements of A. The author proved that A ?1 can only be contained in A if either A is a subfield, or A is the set of trace zero elements in a quadratic extension of a field. Csajbók refined this to the following quantitative statement: if A ?1 ? B, then the bound |A ?1?B| ? 2|B|/q ? 2 holds. He also gave examples showing that his bound is sharp for |B| ? q 3. Our main result is a proof of the stronger bound |A ?1 ? B| ? |B|/q · (1 + O d (q ?1/2)), for |B| = q d with d > 3. We also classify all examples with |B| ? q 3 which attain equality or near-equality in Csajbók’s bound.</p
Inversion and subspaces of a finite field
No full textConsider two F q -subspaces A and B of a finite field, of the same size, and let A ?1 denote the set of inverses of the nonzero elements of A. The author proved that A ?1 can only be contained in A if either A is a subfield, or A is the set of trace zero elements in a quadratic extension of a field. Csajbók refined this to the following quantitative statement: if A ?1 ? B, then the bound |A ?1?B| ? 2|B|/q ? 2 holds. He also gave examples showing that his bound is sharp for |B| ? q 3. Our main result is a proof of the stronger bound |A ?1 ? B| ? |B|/q · (1 + O d (q ?1/2)), for |B| = q d with d > 3. We also classify all examples with |B| ? q 3 which attain equality or near-equality in Csajbók’s bound.</p
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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