[PDF] Top 20 Sets of prime power order generators of finite groups
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Sets of prime power order generators of finite groups
... Proof. By assumption, H is a q-group or H/Φ(H) is a scalar extension. Hence, by Theorem 2.1, all minimal generating sets of H have the same size, say d. Assume d > 2. Since H acts non-trivially on P, by Re- ... See full document
10
The Multiplicative Degree of Some Finite Groups
... group G. This probability is a useful formula to determine how close a subset is to be a subgroup of G. In (Abd Rhani et al., 2016), some upper and lower bounds of this probability are found, when the groups are ... See full document
6
Prime power lie algebras and finite p groups
... of finite nilpotent p-Lie rings and finite p-groups and it is this situation we are interested ...a finite nilpotent p-Lie ring U of nilpotency class less than p, the Campbell Hausdorff ... See full document
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The Power of Group Generators and Relations: An Examination of the Concept and Its Applications
... presenting groups by generators and relations from an original ...free groups, such as Dyck ’ s Theorem , are ...classifying finite groups of a fixed order, representing all ... See full document
20
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 ... See full document
10
On a factorization of an iterated wreath product of permutation groups
... the order |G| of G is defined as |G : 1|. Therefore for every prime p a p-Sylow subgroup 1 of G is a subgroup P such that |P | is a (possibly infinite) power of p and |G : P | is a supernatural ... See full document
13
Power graph of finite abelian groups
... of G. Suppose order of x is not a prime. Without loss of generality, we assume that o(x) = pq, where p, q are distinct primes. Consider the subgroup H =< x >. Since p|o(H), H has an element say y such ... See full document
9
Quasirecognition by prime graph of finite simple groups ${}^2D_n(3)$
... all prime divisors of n. If G is a finite group, then π(|G|) is denoted by ...The prime graph Γ(G) of a finite group G is defined as a graph with vertex set π(G) in which two distinct primes ... See full document
10
A Systematic Approach to Group Properties Using its Geometric Structure
... a finite group, the order product prime graph of a group G, is a graph having the elements of G as its vertices and two vertices are adjacent if and only if the product of their order is a ... See full document
12
Enumeration of some two-generator groups of prime power order
... these groups is w e l l established [see H u p p e r t , 1 9 6 7 , K a p ...every finite p-group is nilpotent but that the converse is not necessarily ...generated groups which have such a series ... See full document
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On almost recognizability by spectrum of simple classical groups
... of sets ρ(2, L) for a finite simple classical group L is contained in [20, Tables 4, ...classical groups are contained in [1, 2], in particular, for every r nonadjacent with 2 in GK(L), there exists ... See full document
27
Bias of group generators in finite and profinite groups: known results and open problems
... This concept actually first arose in the context of field arithmetic. Various theorems that are valid for “almost all” k-tuples in the absolute Galois group G(F ) of a field F appear in [6]. Answering a question of Fried ... See full document
19
Adaptive Power System for Controlling Dynamic Loads of an Induction Motor
... Adaptive Power System products are designed to fill the needs of power conversion for either AC or DC applications. Our AC to AC converters provide frequencies and voltages found around the world for both ... See full document
11
A Study of Pair Encodings: Predicate Encryption in Prime Order Groups
... composite order pairings, which as explained above is very undesirable from an efficiency ...composite order group in which it is embedded, and the proofs that the encodings satisfy this notion are not only ... See full document
41
Finite Simple Graphs and Their Associated Graph Lattices
... any finite graph G = (G, E), the lattice Ω(G) of open sets for the classical topology, partially ordered by subset inclusion, contains a wealth of information about the graph — encoded in an ... See full document
21
Fully Secure Self-Updatable Encryption in Prime Order Bilinear Groups
... in prime order bilinear groups under standard ...in order to make the ciphertext and private key sizes of our SUE scheme polylogarithmic in terms of the maximum time period supported by the ... See full document
22
Brauer relations in finite groups II : quasi elementary groups of order paq
... have primitive relations is that P must be of the form P D K Ì A, where A acts faithfully on C , and in particular is cyclic of order p m , say, A D h h i . Assume that this condition is satisfied. Let K be ... See full document
14
Small semigroup related structures with infinite properties
... There are irreducible units such as the prime numbers in number theory or the finite simple groups of finite group theory, generic examples containing or mimicking the properties of othe[r] ... See full document
220
Presentations : from Kac Moody groups to profinite and back
... proof, which goes from global to local, this difference is crucial: we prove a uniform result for all groups defined over a given global field k (Theorem 3.1), but there is no uniform result over all global fields ... See full document
24
Finite groups with all maximal subgroups of prime or prime square index
... -It now follows that whenever G/G is a subdirect product of primitive solvable groups on a prime or prime square number of letters or if G/G} is any homomorphic image of such a group the[r] ... See full document
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