Compatible pair of nontrivial actions for some cyclic groups of 2-power order

Sulaiman, Sahimel Azwal; Mohamad, Mimi Mohaffyza; Yusof, Yudariah Mohammad; Sarmin, Nor Haniza; Ali, Nor Muhainiah Mohd; Ken, Tan Lit; Ahmad, Tahir

doi:10.1063/1.4907515

Cited by 3 publications

(6 citation statements)

References 3 publications

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“…al (2012) gave the compatibility conditions and the non-abelian tensor product of the cyclic group of order 2 p with the actions of order p. While Sulaiman et al (2015), investigated some compatible pairs of nontrivial actions of order two and four for some cyclic groups of 2-power order. Next, Sulaiman et al (2016) investigated the compatible pair of nontrivial action for finite cyclic 2-groups when two groups are same and the actions are the same order. Lastly, Shahoodh et al (2016) studied the compatible pair of actions for two cyclic groups of 3-power order.…”

Section: G Gmentioning

confidence: 99%

“…al represent the necessary and sufficient conditions for two cyclic groups of 2-power order that compatibly act on each other for the case of G = H. The compatible conditions with the same order of actions are given in the following proposition. Extended from the paper by Sulaiman et al (2016), the results for the numbers of the compatible pair of actions for two cyclic groups of 2-power order are given in the following section.…”

Section: Theoremmentioning

confidence: 99%

“…Sulaiman et al (2016) also gives the exact number of the compatible pair of nontrivial actions for two cyclic groups of 2-power order with the same order of actions.…”

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confidence: 99%

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The Number of Compatible Pair of Actions for Cyclic Groups of 2-Power Order

Azwal

Yusof

Shahoodh

2017

International Journal of Simulation: Systems, Science &Amp; Technology

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The non-abelian tensor product of groups has its origins in the algebraic K-theory and homotopy theory. The nonabelian tensor product for a pair of groups is defined when the actions act compatibly on each other. This research is to determine the maximum number of a compatible pair of actions that can be identified between two cyclic groups of 2-power order for nonabelian tensor product. The compatible pair of actions between two cyclic groups of 2-power order can be found by using the necessary and sufficient conditions of two cyclic groups of 2-power order acting compatibly on each other. Hence, the number of the compatible pair of actions between two cyclic groups of the 2-power order is determined.

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Section: G Gmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

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The Number of Compatible Pair of Actions for Cyclic Groups of 2-Power Order

Azwal

Yusof

Shahoodh

2017

International Journal of Simulation: Systems, Science &Amp; Technology

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“…al [7] gave the compatibility and the nonabelian tensor product of cyclic groups of order 2 p with the actions of order p. Meanwhile, Sulaiman et. al [8] investigated the compatible pairs of nontrivial actions of order two and four for the finite cyclic groups of 2-power order. In [9], Shahoodh et.…”

Section: Introductionmentioning

confidence: 99%

“…al [10] have studied the compatible pair of nontrivial actions for two same finite cyclic 2-groups of 2-power order and provided the exact number of the compatible pair of nontrivial actions for such type groups with the actions that have a same order. In [11], Sulaiman et. al also determined the exact number of the compatible pair of actions for the finite cyclic 2groups when one of the actions has order greater than two.…”

Section: Introductionmentioning

confidence: 99%

The Number of Compatible Pair of Actions for Finite Cyclic Groups of 3-Power Order

Shahoodh

Mohamad

Yusof

et al. 2017

International Journal of Simulation: Systems, Science &Amp; Technology

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Compatible actions are important in determining the non-abelian tensor product. Different compatible pair of actions gives a different tensor product even for the same group. The purpose of this paper is to determine the exact number of compatible pair of actions for the finite cyclic groups of 3-power order. By using some properties of number theory, the number of the compatible pair of actions for finite cyclic groups of 3-power order with a specific order of actions is determined and given as a main result in this paper.

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Number of Compatible Pair of Actions for Finite Cyclic Groups of P-Power Order

et al. 2018

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The compatible actions played an important role before determining the nonabelian tensor product of groups. Different compatible pair of actions gives a different nonabelian tensor product even for the same group. The aim of this paper is to determine the exact number of the compatible pair of actions for the finite cyclic groups of p-power order where p is an odd prime. By using the necessary and sufficient number theoretical conditions for a pair of the actions to be compatible with the actions that have p-power order, the exact number of the compatible pair of actions for the finite cyclic groups of p-power order has been determined and given as a main result in this paper.

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Compatible pair of nontrivial actions for some cyclic groups of 2-power order

Cited by 3 publications

References 3 publications

The Number of Compatible Pair of Actions for Cyclic Groups of 2-Power Order

The Number of Compatible Pair of Actions for Cyclic Groups of 2-Power Order

The Number of Compatible Pair of Actions for Finite Cyclic Groups of 3-Power Order

Number of Compatible Pair of Actions for Finite Cyclic Groups of P-Power Order

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