Ensuring a Group is Weakly Nilpotent

Zarrin, Mohammad

doi:10.1080/00927872.2012.700977

Cited by 10 publications

(7 citation statements)

References 15 publications

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“…Then Azad in [4], obtained a lower bound for ω(N GL(n,q) ) and he determined ω(N P SL (2,q) ). Also the author in [12], shortly prove, determined ω(N P SL(2,q) ) (see Proposition 4.2 of [12]). Clearly, N G is a subgraph of A G and so…”

Section: Introduction and Resultsmentioning

confidence: 99%

Nonnilpotent subsets in the susuki groups

Zarrin

2013

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Let G be a group and N be the class of nilpotent groups. A subset A of G is said to be nonnilpotent if for any two distinct elements a and b in A, a, b ∈ N . If, for any other nonnilpotent subset B in G, |A| ≥ |B|, then A is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by ω(N G ). In this paper, among other results, we obtain ω(N Suz(q) ) and ω(N P GL(2,q) ), where Suz(q) is the Suzuki simple group over the field with q elements and P GL(2, q) is the projective general linear group of degree 2 over the finite field of size q, respectively.

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Section: Introduction and Resultsmentioning

confidence: 99%

Nonnilpotent subsets in the susuki groups

Zarrin

2013

Preprint

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“…This allows us to deduce our main result. With the same argument, combining Theorem 1 with [2, Theorem A] (see also the remark in [2] following the statement of Theorem A), we deduce the following results, the first of which is an improvement of [5,Theorem 3.6].…”

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confidence: 77%

“…An affirmative answer is given in [5] for the class of nilpotent groups. In an earlier paper R. Bryce gave a positive solution for the class of supersoluble groups, under the additional condition n = m. In this short note we prove that an affirmative question can be given whenever X is a class of finite groups which is closed for subgroups, quotient groups and extensions.…”

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confidence: 99%

Applying the Kövári-Sós-Turán theorem to a question in group theory

Lucchini¹

2020

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Let m ≤ n be positive integers and X a class of groups which is closed for subgroups, quotient groups and extensions. Suppose that a finite group G satisfies the condition that for every two subsets M and N of cardinalities m and n, respectively, there exist x ∈ M and y ∈ N such that x, y ∈ X.Let m, n be positive integers and X be a class of groups. We say that a group G satisfies the condition X(m, n) if for every two subsets M and N of cardinalities m and n, respectively, there exist x ∈ M and y ∈ N such that x, y ∈ X. If G satisfies the condition X(m, n), then we write G ∈ X(m, n). In [5] M. Zarrin proposed the following question.

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“…What relations among m, n, and |G| guarantee that G is abelian? In [1] it is shown that all infinite C(m, n)-groups are abelian, hence the commutativity question is essentially interesting for finite groups (see also [5]). …”

Section: Introductionmentioning

confidence: 98%