conjugacy class sizes
Finite groups with the same conjugacy class sizes as a finite simple group
... Proof. (i) By Lemma 2.5, | S | | | G/Z(G) | . Now let there exist q ∈ π(G/Z (G)) − π(S). Then since q ∤ | S | , we get that q does not divide any conjugacy class sizes of G and hence, Lemma 2.1 ...
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On finite groups with square-free conjugacy class sizes
... of conjugacy class sizes on the structure of finite groups has been thoroughly ...the conjugacy class sizes: when they are ...
8
On p regular G conjugacy class sizes
... In a recent paper [], the authors studied the structure of G under the condition that the largest two p-regular conjugacy class sizes (say, m and n) of G are coprime, where m > n and p n. Notice ...
9
One-prime power hypothesis for conjugacy class sizes
... Abstract. A finite group G satisfies the one-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes m and n are either equal or have common divisor a ...
7
Conjugacy classes and graphs of two-groups of nilpotency class two
... of conjugacy classes, conjugacy class sizes and graphs related to conjugacy classes are compared and ...of class two and the application of GAP in this research are given in this ...
24
On bipartite divisor graph for character degrees
... set X ∗ and two vertices m and n are connected if gcd(m, n) > 1. Motivated by [3], in this paper, we introduce the bipartite divisor graph for character degrees of a finite group and obtain some properties of this ...
7
Bipartite divisor graph for the set of irreducible character degrees
... of conjugacy class sizes of a finite group and studied various properties of ...of conjugacy class sizes have diameter exactly ...of conjugacy class sizes is ...
11
Conjugacy and order classes of two-generator p-groups of nilpotency class two
... Studies on the bounds of the number of conjugacy classes done by a number of researchers are reviewed. The classification of 2-generator p-groups of class 2 (p an odd prime) is stated and elaborated. Then, ...
16
The conjugacy classes of metabelian groups of order at most 24
... non-central conjugacy classes of order greater than one, namely 5, and the metabelian groups types (13), (15), (16) and (17) also have the same number of conjugacy classes which is 10 as well as non-central ...
5
Recognizing L2(p) by its order and one special conjugacy class size
... In the past thirty years, many authors investigated some quantitative characterizations of finite groups, especially finite simple groups, such as quantitative characterizations by group order and element orders, by the ...
10
Absent Data Generating Classifier for Imbalanced Class Sizes
... We propose an algorithm for two-class classification problems when the training data are imbalanced. This means the number of training instances in one of the classes is so low that the conventional classification ...
30
The exact number of conjugacy classes for 2 - generator p - groups of nilpotency class 2
... The major contribution of this thesis will be the new theoretical results on the exact number of conjugacy classes for 2-generator p-groups of class 2 (p an odd prime). This thesis also contributes to a ...
17
Class sizes in primary schools in Wales : September 2011
... Last year the number of infant classes of over 30 pupils (and pupils within such classes) increased; there was a corresponding increase in the number of junior classes of over 30 pupils. The total number of infant and ...
10
\mathversion{bold}ON NON-ABELIAN GROUPS OF ORDER $2^n$, $n\geq 4$ USING \textsf{GAP}
... Let G be a finite group, and x ∈ G with o(x) = k. Then, we need to count all y ∈ G which has the same order as x. Precisely, we will determined a class of each order. The set of all of these classes is called the ...
12
Hecke Groups, Dessins d’Enfants and the Archimedean Solids
... well-known class of convex polyhedra are the Archimedean solids: the semi-regular convex polyhedra composed of two or more types of regular polygons meeting in identical vertices, with no requirement that faces be ...
29
Primitive stability and Bowditch conditions for rank 2 free group representations
... Remark 2.5. Observe that the two conditions above are invariant under conjugacy in P SL(2, C ), hence it makes sense to speak about classes in the character variety satisfying these requirements. The second BQ ...
65
Asymptotics in conjugacy classes for free groups
... In the same setting as his prime geodesic theorem, Huber [25] also established asymptotic results for certain groups of isometries of the hyperbolic plane. Here the connection to the prime geodesic theorem is as follows. ...
105
Classification of involutions of SL(n,k) and SO(2n+1,k)
... For k = R the group SO(2n + 1, k) is k-anisotropic, so there are no (θ, k)-split tori, so consequently also no k-inner elements. By [Hel88, Lemma 10.3] the isomorphy classes of involutions of k-anisotropic real groups ...
92
Maximal length elements of excess zero in finite Coxeter Groups
... the group of signed permutations; that is, permutations w of {1, . . . , n, −1, . . . , −n} such that w(−i) = −w(i) for 1 ≤ i ≤ n. Signed permutations can be written as permutations where each number has either a plus or ...
17
The Perception and Attitudes of Teachers Towards Class Sizes in Secondary Schools
... Teachers say that teaching in smaller classes improve student-teacher relationship, strengthens the connection between a teacher and his/her student, making the experience much more enjoyable and meaningful to all ...
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