Symmetric designs and projective special linear groups of dimension at most four
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DOI: 10.1002/jcd.21738
Abstract: In this article, we study symmetric ( v , k , λ ) designs admitting a flag‐transitive and point‐primitive automorphism group G whose socle is isomorphic to a projective special linear group of dimension at… read more here.
Keywords: symmetric designs; designs projective; special linear; dimension four ... See more keywords
Universal Equivalence of Linear Groups Over Local Commutative Rings with 1/2
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DOI: 10.1007/s10469-019-09552-0
Abstract: It is proved that the universal equivalence of general or special linear groups of orders greater than 2 over local commutative rings with 1/2 is equivalent to the coincidence of orders of groups and universal… read more here.
Keywords: commutative rings; linear groups; universal equivalence; equivalence linear ... See more keywords
On the number of derangements and derangements of prime power order of the affine general linear groups
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DOI: 10.1007/s10801-016-0709-3
Abstract: A derangement is a permutation that has no fixed points. In this paper, we are interested in the proportion of derangements of the finite affine general linear groups. We prove a remarkably simple and explicit… read more here.
Keywords: derangements prime; linear groups; power order; general linear ... See more keywords
Isomorphisms of the linear groups GL2(R) over associative rings R
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DOI: 10.1016/j.jalgebra.2017.11.025
Abstract: Abstract Isomorphisms of the linear groups GL 2 ( R ) over associative rings R with 1/2 and 1/3 are considered. In particular, we give a full description of automorphisms φ : GL 2 (… read more here.
Keywords: associative rings; linear groups; groups gl2; isomorphisms linear ... See more keywords
Class 2 quotients of solvable linear groups
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DOI: 10.1016/j.jalgebra.2018.03.031
Abstract: Let $G$ be a finite group, and let $V$ be a completely reducible faithful $G$-module. By a result of Glauberman it has been known for a long time that if $G$ is nilpotent of class… read more here.
Keywords: linear groups; class; class quotients; solvable linear ... See more keywords
On group rings of linear groups
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DOI: 10.1016/j.jpaa.2016.05.015
Abstract: Abstract Let H be a finitely generated group of matrices over a field F of characteristic zero. We consider the group ring KH of H over an arbitrary field K whose characteristic is either zero… read more here.
Keywords: linear groups; field; group; rings linear ... See more keywords
Engel subnormal subgroups of skew linear groups
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DOI: 10.1016/j.laa.2018.08.020
Abstract: Abstract Let D be a division ring with uncountable center and n a natural number. In this article we show that every Engel subnormal subgroup of GL n ( D ) is central. This affirmatively… read more here.
Keywords: engel subnormal; subgroups skew; linear groups; skew linear ... See more keywords
Representation stability and finite linear groups
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DOI: 10.1215/00127094-2017-0008
Abstract: We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications… read more here.
Keywords: linear groups; group; representation stability; general linear ... See more keywords