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Regular integral models for Shimura varieties of orthogonal type
We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular $p$-adic integral models for these varieties over odd primes $p$ at which the level subgroup is the connected stabilizer of a vertex lattice in the orthogonal space. Our construction is obtained by combining results of Kisin and the first author with an explicit presentation and resolution of a corresponding local model.
Journal Article
Correction to: Identifying high risk subgroups of MSM: a latent class analysis using two samples
Following publication of the original article [1], the author reported his family name has been marked as the first name. His given name is M. Kumi and his family name is Smith.
Journal Article
On the character table of non-split extension 26.S 8
Problem Statement & Objective: Character tables of maximal subgroups of finite simple groups provide considerable amount of information about the groups. In the present article, our objective is to compute the character table of one maximal subgroup of the orthogonal group \\(PS{O}_{8}^{+}(3)\\). Approach: The projective special orthogonal group \\(PS{O}_{8}^{+}(3)\\cong {O}_{8}^{+}(3){.2}_{1}\\) is obtained from the special orthogonal group \\(S{O}_{8}^{+}(3)\\) on factoring by the group of scalar matrices it contains. The group \\({O}_{8}^{+}(3){.2}_{1}\\) has a maximal subgroup of the form 26.S 8 with index 3838185. The group Q ≅ 26 · S 8 is a non-split group extension of an elementary abelian 2-group of order 64 by the symmetric group S 8. We apply the Fischer-Clifford theory to compute the irreducible characters of the extension 26 · S 8. Results and Conclusion: We produce 64 conjugacy classes of elements as well as 64 irreducible character of the non-split group extension 26 · S 8 corresponding to the three inertia factors H 1 = S 8, H 2 = S 6 × 2 and H 3 = (S 4 × S 4):2.
Journal Article
New Facts about the Vanishing Off Subgroup
Abstract
In this manuscript, we generalize Lewis’s result about a central series associated with the vanishing off subgroup. We write
$V_{1}=V(G)$
for the vanishing off subgroup of
$G$
, and
$V_{i}=[V_{i-1},G]$
for the terms in this central series. Lewis proved that there exists a positive integer
$n$
such that if
$V_{3}
Journal Article
Mixed and Non-mixed Normal Subgroups of Dihedral Groups Using Conjugacy classes
In this paper, we characterize and compute the mixed and non-mixed basis of Dihedral groups. Also, by computing the conjugacy classes, we describe all the mixed and non-mixed normal subgroups of Dihedral Groups.
Journal Article
The Projective Character Tables of a Solvable Group 26:6×2
The Chevalley–Dickson simple group G24 of Lie type G2 over the Galois field GF4 and of order 251596800=212.33.52.7.13 has a class of maximal subgroups of the form 24+6:A5×3, where 24+6 is a special 2-group with center Z24+6=24. Since 24 is normal in 24+6:A5×3, the group 24+6:A5×3 can be constructed as a nonsplit extension group of the form G¯=24·26:A5×3. Two inertia factor groups, H1=26:A5×3 and H2=26:6×2, are obtained if G¯ acts on 24. In this paper, the author presents a method to compute all projective character tables of H2. These tables become very useful if one wants to construct the ordinary character table of G¯ by means of Fischer–Clifford theory. The method presented here is very effective to compute the irreducible projective character tables of a finite soluble group of manageable size.
Journal Article
Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p 3
Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonmetacyclic of order p3. In this paper, the P1-groups are classified, and as a by-product, we prove the Hughes’ conjecture is true for the P1-groups.
Journal Article
The Maximal Subgroups of the Low-Dimensional Finite Classical Groups
This book classifies the maximal subgroups of the almost simple finite classical groups in dimension up to 12; it also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q). Theoretical and computational tools are used throughout, with downloadable Magma code provided. The exposition contains a wealth of information on the structure and action of the geometric subgroups of classical groups, but the reader will also encounter methods for analysing the structure and maximality of almost simple subgroups of almost simple groups. Additionally, this book contains detailed information on using Magma to calculate with representations over number fields and finite fields. Featured within are previously unseen results and over 80 tables describing the maximal subgroups, making this volume an essential reference for researchers. It also functions as a graduate-level textbook on finite simple groups, computational group theory and representation theory.
eBook
On commuting automorphisms of finite p-groups of co-class 3, when p > 2
Let G be a group. An automorphism a of G is called a commuting automorphism if α(g),g] = 1 for all g ∈ G. Let A(G) denote the set of all commuting automorphisms of G. A group G is said to be an A(G)-group if A(G) forms a subgroup of Aut(G), where Aut(G) denotes the group of all automorphisms of G. In [Proc. Japan Acad. Ser. A Math. Sci. 91(2015), no. 5, 57-60] Rai proved that a finite p-group G of co-class 2 for an odd prime p is an A(G)-group. We prove that a finite p-group G of co-class 3 for an odd prime p, under some conditions, is an A(G)-group.
Journal Article
On linear cyclically ordered subgroups of cyclically ordered groups
Given a group G equipped with a cyclic order so that G is cyclically ordered group. In this condition, all subgroups of G are cyclically ordered. When the group G is finite the cyclic order on G is not linear, even when the group G is infinite, the cyclic order on G is not necessarily linear. In this article we discuss an infinite group G and some conditions so that there is a subgroup H of G in which the cyclic order on H is also linear. The positive cone P(H) of H is then a semigroup, meanwhile the positive cone P(G) of G is not a semigroup.
Journal Article