[PDF] Top 20 Universidad Nacional Mayor de San Marcos Informe Final n3
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Finite groups with some $SS$-embedded subgroups
... all subgroups, independently of whether they are normal, s-permutable, c-normal, nearly s-normal or S-embedded in G are SS-embedded subgroups of ...is SS-embedded in G, ... See full document
24
Finite groups with given $\\sigma$ embedded and $\\sigma$ $n$ embedded subgroups
... have that (|HE ∩ T : H ∩ T|, |HE ∩ T : E ∩ T |) = (|(HE ∩ T )H : H|, |(HE ∩ T )E : E|) = 1. Hence HE ∩ T = (H ∩ T )(E ∩ T ) by [11, Chapter A, 1.6(b)]. Then HE ∩ T = (H ∩ T )(E ∩ T ) ≤ HE σG ≤ (HE) σG by Lemma 2.3(4). ... See full document
25
On weakly $SS$-quasinormal and hypercyclically embedded properties of finite groups
... By Lemma 2.5, we may assume that P is not cyclic. Let M be a proper subgroup of G, L a cyclic subgroup of P ∩ M with order p or 4 (if p = 2 and P is non-abelian) having no p-nilpotent supplement in M , then L has no ... See full document
25
Partially $S$-embedded minimal subgroups of finite groups
... assuming that some subgroups of G satisfy the S-embedded property, many meaningful results have been derived (see [8], [10] etc.), a series of known results in the literature were generalized. As ... See full document
37
Finite groups with cyclic Sylow subgroups for all odd primes
... normalizer of X in G. Let N^ be a Sylow 2-subgroup of N(X) containing V<s>. Then N^ is either dihedral or semi- dihedral since the only other subgroups of a semi-dihedral group are either cyclic or ... See full document
20
The number of maximal subgroups and probabilistic generation of finite groups
... All groups in this survey will be finite. Let G be a d-generated group. The motivating question of this paper is: How many elements one should expect to choose uniformly and randomly to generate G? Let us ... See full document
67
Generalizing quasinormality
... quasinormal subgroups H of any group G, a lot of information has been discovered when H is ...all subgroups of H are quasinormal in G (see [8], ...is finite of odd order or even infinite, then [H, G] ... See full document
13
Minimal conditions on Clifford semigroup congruences
... If X is a nonempty subset of a group G, the normal closure of X in G, denoted by X G , is the intersection of all normal subgroups of G which contains X. Dually, the core of X in G, denoted by X G , is the join of ... See full document
29
On some invariants of finite groups
... Proposition 2.11 ([12], Proposition 4.4). Let G be a group with the basis property. Then G/Φ(G) is a semidirect product constructed via the multiplication on some vector space over a finite field. ... See full document
88
Near Frattini subgroups of residually finite generalized free products of groups
... Similar results for the (lower) near Frattini subgroups of such generalized free prod- ucts of groups are produced in [2, 3, 4, 5, 6, 7, 8, 9]. In this paper which is motivated by R. B. J. T. Allenby and C. ... See full document
9
Intersection graph of subgroups of some non-abelian groups
... of subgroups of a group G is a graph whose vertex set is the set of all proper subgroups of G and two distinct vertices are adjacent if and only if their intersection is ...of subgroups of dihedral ... See full document
15
On free subgroups of finite exponent in circle groups of free nilpotent algebras
... In [4], Magnus investigated the groups of units in the Z -algebra of power series on a non-empty set X. He showed that the subgroup generated by { 1 + x | x ∈ X } is a free group, freely generated by this set. In ... See full document
183
On some aspects of finite soluble groups
... Proof. Assume the result is false and let ^ be a meta-nilpotent Fischer class which is not s-closed. Let G be a group of minimal order among those ^-groups which have subgroups not belonging to ^ . Choose ... See full document
6
Some groups of finite homological type
... are finite models for BH and for BK. If there is a model for BL with finite 1-skeleton, then by gluing BH, BL × I and BK , one may construct a model for BG with finite ... See full document
14
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
26
On the Number of Distinct Fuzzy Subgroups for Some Elementary Abelian Groups and Quaternion Groups
... fuzzy subgroups of Z p × Z p and the number of chains of subgroups of Z p × Z p that ends in Z p × Z p fixed for a particular element f k ∈ Aut( Z p × Z p ... See full document
17
Finite non-nilpotent groups with few non-normal non-cyclic subgroups
... the Sylow subgroups of G of odd order are non-normal in G. Thus all of their normalizers are cyclic. By Burnside’s theorem, G has a normal q-complement for each odd prime q ∈ π(G). The intersection of all of these ... See full document
17
On finite groups having a certain number of cyclic subgroups
... We summarize our notations. cl(a) denotes the conjugacy class of a in G, π(G) denotes the set of prime numbers dividing the order of G, ϕ(n) denotes the Euler function that counts the positive integers less than n that ... See full document
150
Model subgroups of finite soluble groups
... where t is the number o f involutions in G, and consequently by a result of Frobenius and Schur [1, Corollary 4.6, page 51] every irreducible character o f G is afforded by a real representation. From here Baddeley [12] ... See full document
102
On the semi cover-avoiding property and $\mathcal{F}$-supplementation
... Lemma 2.7. [18, Lemma 2.6] Let H 6= 1 be a solvable normal subgroup of a group G. If every minimal normal subgroup of G which is contained in H is not contained in Φ(G), then the Fitting subgroup F (H) of H is the direct ... See full document
128
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