[PDF] Top 20 Finite groups with the same conjugacy class sizes as a finite simple group
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Finite groups with the same conjugacy class sizes as a finite simple group
... a group H if π(O(x)) ⊆ π (π(O(x)) ⊆ π(H) − π). For a group G, the prime graph GK(G) of G is a simple graph whose vertices are the prime divisors of the order of G and two distinct prime numbers p and ... See full document
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On finite groups with square-free conjugacy class sizes
... Only finite groups will be considered in this expository ...of conjugacy class sizes on the structure of finite groups has been thoroughly ...the conjugacy ... See full document
8
Some problems about products of conjugacy classes in finite groups
... a finite simple group of Lie type and A and B are non-trivial conjugacy classes, either both semisimple or both unipotent, then AB is not a conjugacy ...for simple algebraic ... See full document
10
Character expansiveness in finite groups
... a finite group G is conjugacy expansive if for any normal subset S and any conjugacy class C of G the normal set SC consists of at least as many conjugacy classes of G as S ...a ... See full document
9
On almost recognizability by spectrum of simple classical groups
... a finite group G, the spectrum of G is the set of its element orders and is denoted by ...ω(G). Finite groups are said to be isospectral if their spectra ...a finite group G has ... See full document
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Conjugacy classes contained in normal subgroups: an overview
... to conjugacy classes of normal subgroups in finite groups In 1990, ...the sizes of the ordinary conjugacy classes of G as follows: the vertices of Γ(G) are represented by the ... See full document
14
On base sizes for actions of finite classical groups
... a finite almost simple classical group and let Ω be a faithful primitive non-standard ...such groups G, and the existence of such an undetermined constant has been established by Liebeck and ... See full document
25
Centralizers in simple locally finite groups
... by finite group ...infinite simple group. Recall that a group X involves an infinite simple group if there exist subgroups A and B of X such that A C B and B/A is ... See full document
10
Conjugacy classes and graphs of two-groups of nilpotency class two
... the conjugacy classes on the structure of a finite group have been the subject of research over the ...the conjugacy class sizes depend on the order of the commutator ... See full document
24
A note on maximal length elements in conjugacy classes of finite coxeter groups
... The maximal lengths of elements in each of the conjugacy classes of Coxeter groups of types B n , D n and E 6 are determined. Additionally, representative elements are given that attain these maximal ... See full document
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Conjugacy separability of certain HNN extensions with normal associated subgroups
... the class-preserving automorphisms of a finitely generated conjugacy separable group G are inner, then the outer automorphism group of G is residually ...automorphism groups are ... See full document
16
CH-groups which are finite $p$-groups
... the group G a CH-group if the conjugacy class lengths of any two commuting noncentral elements of G are ...AC- groups) in which centralisers of noncentral elements are abelian or ... See full document
15
Sylow like theorems for $V(\mathbb{Z}G)$
... for groups of order six SIP is an open ...specific class of groups ...integral group rings of finite nonabelian simple ... See full document
11
One-prime power hypothesis for conjugacy class sizes
... with r dividing |x G | and s dividing |z G | but the product rs does not divide any conjugacy class size in G. Thus, by [9, Prop. 5.1], G has a normal r-complement (say), call this complement N . Then N ... See full document
7
The status of the Zassenhaus conjecture for small groups
... The HeLP package also gives the spectrum for the torsion unit under each irreducible representation of the group. This information is equivalent to the partial augmentation information. It is used directly in the ... See full document
10
Vol 2013
... all finite simple groups except symplectic group and or- thogonal group of odd dimension with order larger than 10 8 ...the groups under ... See full document
7
A Simple Classification of Finite Groups of Order p2q2
... a finite number of elements is called Galois field. A finite field of order q exists if and only if the q is a prime power p k where p is a prime number and k is a positive ...a finite field with q = ... See full document
10
Rationality of blocks of quasi-simple finite groups
... Donovan’s conjecture is open in the general case, but there are certain situations where it is known to hold. This is discussed in more detail in Section 2.3. There exists a weaker version of Donovan’s conjecture, known ... See full document
134
On bipartite divisor graph for character degrees
... Proof. Suppose that p ∈ π(|G|) then by hypothesis we have p ∈ ρ(G) and therefore, p is one of the vertices of B(G). Since B(G) is a complete bipartite graph therefore, p is connected to every element of cd ∗ (G) which ... See full document
7
Groups with the same orders of Sylow normalizers as the Mathieu groups
... There exist many characterizations for the sporadic simple groups. In this paper we give two new characterizations for the Mathieu sporadic groups. Let M be a Mathieu group and let p be the ... See full document
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