Two generator p-groups of nilpotency class 2 and their conjugacy classes

Ahmad, Azhana; Magidin, Arturo; Morse, Robert Fitzgerald

doi:10.5486/pmd.2012.5114

Cited by 22 publications

(15 citation statements)

References 8 publications

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“…They were recently classified by Ahmad, Magidin and Morse [2], although we will not use their classification theorems. Let G be any 2-generator p-group of class 2 of order p n .…”

Section: Noether's Problem For Groups Of Nilpotency Classmentioning

confidence: 99%

Bogomolov multipliers for some p-groups of nilpotency class 2

Michailov¹

2016

Acta. Math. Sin.-English Ser.

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Abstract. The Bogomolov multiplier B 0 (G) of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality of the Bogomolov multiplier is an obstruction to Noether's problem. We show that if G is a central product of G 1 and G 2 , regarding K i ≤ Z(G i ), i = 1, 2, and θ : G 1 → G 2 is a group homomorphism such that its restriction θ| K1 : K 1 → K 2 is an isomorphism, then the triviality of B 0 (G 1 /K 1 ), B 0 (G 1 ) and B 0 (G 2 ) implies the triviality of B 0 (G). We give a positive answer to Noether's problem for all 2-generator p-groups of nilpotency class 2, and for one series of 4-generator p-groups of nilpotency class 2 (with the usual requirement for the roots of unity).

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“…They were recently classified by Ahmad, Magidin and Morse [2], although we will not use their classification theorems. Let G be any 2-generator p-group of class 2 of order p n .…”

Section: Noether's Problem For Groups Of Nilpotency Classmentioning

confidence: 99%

Bogomolov multipliers for some p-groups of nilpotency class 2

Michailov¹

2016

Acta. Math. Sin.-English Ser.

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“…The Classification. [4] Let ‫‬ be a prime and ݊ ʹ a positive integer. Every ʹ-generated ‫-‬group of class exactly two of order ‫‬ corresponds to an ordered ͷ-tuple of integers ሺߙǡ ߚǡ ߛǢ ߩǡ ߪሻǡ such that:…”

Section: Groups Of Class Twomentioning

confidence: 99%

Specific automorphisms on a 2-generated p-group of class two

Sarmin

Barakat

2013

AIP Conference Proceedings

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Let ‫ܩ‬ be a finite two generated ‫-‬group of nilpotency class two, where ‫‬ is a prime number. If ߶ሺ‫ܩ‬ሻ is the Frattini subgroup of ‫,ܩ‬ then ‫ܩ‬ ߶ሺ‫ܩ‬ሻ Τ is a vector space of dimension two over the field Ժ ‫‬Ժ Τ . In this paper, we determine those automorphisms on ‫ܩ‬ which induce identity transformation on ‫ܩ‬ ߶ሺ‫ܩ‬ሻ Τ . We use the most updated classification given for ‫ܩ‬ to find these automorphisms. The results of this study are applicable in classifying ‫,‪ሻ‬ܩ‪ሺ‬ݐݑܣ‬ the automorphism group of ‫.ܩ‬

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“…The conjugacy classes of p-groups, with an abelian subgroup of index p, with |Z(G)| = |G′|, were studied in (Pantea, 2004). Zapirain (2011) established a lower bound for the number of conjugacy classes of finite nilpotent groups using the group size multiply by a certain constant c. Recently, Ahmad et al (2012) obtained general formulas to find the number of conjugacy classes of 2-generator p-groups of class 2.…”

Section: Introductionmentioning

confidence: 99%

An Upper Bound to the Number of Conjugacy Classes of Non-Abelian Nilpotent Groups

Al-Hasanat

Al-Dababseh

Al-Sarairah

et al. 2017

Journal of Mathematics and Statistics

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Abstract:The number of conjugacy classes of symmetric group, dihedral group and some nilpotent groups is obtained. Until now, it has not been obtained for all nilpotent groups. Although there are some lower bounds to this value, there is no non-trivial upper bound. This paper aims to investigate an upper bound to this number for all finite nilpotent groups. Moreover, the exact number of conjugacy classes is found for a certain case of non-abelian nilpotent groups.

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Two generator p-groups of nilpotency class 2 and their conjugacy classes

Abstract: We give a classification of two-generator p-groups of nilpotency class 2. Using this classification, we give a formula for the number of such groups of order p n in terms of the partitions of n of length 3, and find formulas for the number and size of their conjugacy classes.

Cited by 22 publications

References 8 publications

Bogomolov multipliers for some p-groups of nilpotency class 2

Bogomolov multipliers for some p-groups of nilpotency class 2

Specific automorphisms on a 2-generated p-group of class two

An Upper Bound to the Number of Conjugacy Classes of Non-Abelian Nilpotent Groups

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