[PDF] Top 20 On p regular G conjugacy class sizes
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On p regular G conjugacy class sizes
... Let N be a normal subgroup of a p-solvable group G. The purpose of this paper is to investigate some properties of N under the condition that the two longest sizes of the non-central ... See full document
9
Recognizing L2(p) by its order and one special conjugacy class size
... Lemma . Let G be a simple group with a disconnected prime graph. Then its order com- ponents are exhibited in Tables -, where p is an odd prime and q is a prime power. Proof By [, , ] and the ... See full document
10
cycle indices, subdegrees and suborbital graphs of PSL(2,q) acting on the cosets of some of its subgroups
... of conjugacy class of elements g ∈ G with certain subgroups of G, are used to determine the disjoint cycle structure of g and hence cycle index of G corresponding to some ... See full document
139
Conjugacy and order classes of two-generator p-groups of nilpotency class two
... Let G be a group with identity element e and x, y ∈ ...element g ∈ G such that g −1 xg = x g = ...on G. It is reflexive since x e = x and symmetric since if x g = y then x ... See full document
16
Connected components of the category of elementary abelian $p$ subgroups
... of conjugacy classes of maximal elementary abelian subgroups of rank 2 in a finite p-group G, for an odd prime ...is p if G has rank at least 3 and it is p + 1 if G has ... See full document
7
The exact number of conjugacy classes for 2 - generator p - groups of nilpotency class 2
... Let G be a group with the identity element e and x, y ∈ ...in G if there exists an element g ∈ G such that g −1 xg = x g = ...on G. This equivalence relation induces a ... See full document
17
Finite groups with the same conjugacy class sizes as a finite simple group
... Theorem 2.14. If S is one of the groups in Table 1 (up to isomorphism), then G ∼ = S × Z(G). Proof. Since S is OC-characterizable, by the references stated in the third column of Table 1, we deduce from ... See full document
11
Algebra in the Stone-\(\check{C}\)ech compactification: applications to topologies on groups
... group G such that the topology of G is maximal in the class of all regular left invariant topologies on G, then there is a P -point in ω ∗ ... See full document
28
On Some Problems in Group Theory of Probabilistic Nature
... where G is a 2-generator 2-groups of nilpotency class 2 up to order 64, using the fact that the probability is the number of conjugacy classes divided by the order of the ...probability P n ... See full document
7
Conjugacy classes contained in normal subgroups: an overview
... the class sizes of G, and two vertices p and q are joined by an edge if there exists a conjugacy class in G whose size is a multiple of ...groups G for which the ... See full document
14
The irreducible subgroups of exceptional algebraic groups
... each G; these are Tables 1A–5A. Each row of the table gives a conjugacy class of G-irreducible connected subgroups, with the first column giving the ID number, the second column the ... See full document
197
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 ... See full document
11
New examples of mixed Beauville groups
... for G when q ≥ 11 and since gcd(p, q − ) = 1 we immediately have, by Lemma 16, a hyperbolic generating triple for G × ...for G of type (q + , q + , q + ) and note that both p and q − ... See full document
24
One-prime power hypothesis for conjugacy class sizes
... to G satisfying the one-prime power hypothesis, that is, if m and n are distinct non-trivial conjugacy class sizes of G then either m and n are coprime or their greatest common divisor ... See full document
7
On finite groups with square-free conjugacy class sizes
... to conjugacy class sizes of some elements of a group not divisible by p 2 , for some fixed prime ...square-free class sizes for all ...of conjugacy class ... See full document
8
The commutativity degree of some nonabelian two-groups with a cyclic subgroup of index four
... In the past years, the probabilistic theory was proved to be beneficial in the solution of different complicated problems in group theory. The question that come arised from the previous researches was “Can someone ... See full document
19
Maximal length elements of excess zero in finite Coxeter Groups
... there is at least one (usually many) elements of maximal length and excess zero in every conjugacy class. Finally it is easy to check that every element of the dihe- dral group has excess zero, so the ... See full document
17
On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups
... centric connectivity index of Γ G for every non-abelian finite group G in terms of the number of conjugacy classes k ( G ) and the size of the group G.. Keywords: non-commuting graph, ec[r] ... See full document
7
Groups with context free co word problem
... the class of regular languages is closed under complementation, groups with regular co-word problem are precisely the ones with regular word problem, or equivalently all finite groups ... See full document
16
Class sizes (SPICe briefing; 11/09)
... on class sizes, free school meals and pre-school nursery hours (Scottish Government ...lower class sizes remained, this agreement set out a target for progress by August ... See full document
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