A new maximal subgroup of 𝐸₈ in characteristic 3

AbstractLet 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1_{H})^{G} for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.

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PROPER ACTIONS ON SOME EXPONENTIAL SOLVABLE HOMOGENEOUS SPACES

International Journal of Mathematics ◽

10.1142/s0129167x0500317x ◽

2005 ◽

Vol 16 (09) ◽

pp. 941-955 ◽

Cited By ~ 12

Author(s):

ALI BAKLOUTI ◽

FATMA KHLIF

Keyword(s):

Maximal Subgroup ◽

Homogeneous Space ◽

Lie Group ◽

Homogeneous Spaces ◽

Intersection Property ◽

Nilpotent Lie Group ◽

Proper Actions ◽

Simply Connected

Let G be a connected, simply connected nilpotent Lie group, H and K be connected subgroups of G. We show in this paper that the action of K on X = G/H is proper if and only if the triple (G,H,K) has the compact intersection property in both cases where G is at most three-step and where G is special, extending then earlier cases. The result is also proved for exponential homogeneous space on which acts a maximal subgroup.

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The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

Algebra Colloquium ◽

10.1142/s1005386710000386 ◽

2010 ◽

Vol 17 (03) ◽

pp. 389-414 ◽

Cited By ~ 4

Author(s):

Faryad Ali ◽

Jamshid Moori

Keyword(s):

Automorphism Group ◽

Conjugacy Class ◽

Maximal Subgroup ◽

Computer Algebra ◽

Character Table ◽

Computer Algebra Systems ◽

Split Extension ◽

Sporadic Group ◽

Local Subgroup ◽

Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

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Maximal subgroups of finite groups

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117129000045x ◽

1990 ◽

Vol 13 (2) ◽

pp. 311-314

Author(s):

S. Srinivasan

Keyword(s):

Maximal Subgroup ◽

Finite Groups ◽

Maximal Subgroups ◽

Fitting Subgroup ◽

Small Index

In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting subgroup of the group.

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Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700023636 ◽

1985 ◽

Vol 38 (3) ◽

pp. 330-350 ◽

Cited By ~ 15

Author(s):

D. F. Holt ◽

N. Spaltenstein

Keyword(s):

Finite Field ◽

Lie Algebras ◽

Closed Field ◽

Nilpotent Orbits ◽

Reductive Algebraic Group ◽

Exceptional Lie Algebras ◽

Closed Fields ◽

Characteristic 3 ◽

Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

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Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3

Journal of Algebra and Its Applications ◽

10.1142/s0219498819500695 ◽

2019 ◽

Vol 18 (04) ◽

pp. 1950069

Author(s):

Qian Liu ◽

Yujuan Sun

Keyword(s):

Positive Integer ◽

Finite Field ◽

Coding Theory ◽

Permutation Polynomials ◽

Combinatorial Designs ◽

Dickson Polynomial ◽

Niho Exponents ◽

Characteristic 3 ◽

Permutation Trinomials ◽

Algebraic Forms

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. Permutation trinomials attract people’s interest due to their simple algebraic forms and additional extraordinary properties. In this paper, based on a seventh-degree and a fifth-degree Dickson polynomial over the finite field [Formula: see text], two conjectures on permutation trinomials over [Formula: see text] presented recently by Li–Qu–Li–Fu are partially settled, where [Formula: see text] is a positive integer.

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Taro vein chlorosis virus: characterization and variability of a new nucleorhabdovirus

Journal of General Virology ◽

10.1099/vir.0.80591-0 ◽

2005 ◽

Vol 86 (2) ◽

pp. 491-499 ◽

Cited By ~ 44

Author(s):

Peter Revill ◽

Xuan Trinh ◽

James Dale ◽

Rob Harding

Keyword(s):

Pacific Islands ◽

New Caledonia ◽

Solomon Islands ◽

N Gene ◽

Nucleotide Level ◽

Putative Gene ◽

Intergenic Regions ◽

Rna Genome ◽

Characteristic 3 ◽

High Level

Sequencing of the monopartite RNA genome of a Fijian isolate of Taro vein chlorosis virus (TaVCV) confirmed that it is a definitive rhabdovirus with most similarity to members of the genus Nucleorhabdovirus. The TaVCV 12 020 nt negative-sense RNA genome contained six ORFs in the antigenomic sequence, equivalent to the N, P, 3, M, G and L genes that have been identified in other rhabdoviruses. The putative gene products had highest similarity to those of the nucleorhabdovirus Maize mosaic virus. A characteristic 3′-AAUUCUUUUUGGGUUGU/A-5′ sequence was identified in each of the intergenic regions and the TaVCV leader and trailer sequences comprised 140 and 61 nt, respectively. Assignment of TaVCV to the genus Nucleorhabdovirus was supported by thin-section electron microscopy of TaVCV-infected taro leaves, which identified virions budding from nuclear membranes into the perinuclear space. Variability studies identified high levels of TaVCV sequence diversity. Within the L gene of 20 TaVCV isolates from Fiji, the Federated States of Micronesia, New Caledonia, Papua New Guinea, Solomon Islands and Vanuatu, maximum variability at the nucleotide level was 27·4 %. Within the N gene, maximum variability among 15 isolates at the nucleotide level was 19·3 %. The high level of TaVCV variability observed suggested that the introduction of TaVCV to the Pacific Islands was not a recent occurrence.

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