As applications of the computingformulae, we also obtain several bounds forPrg(H,Aut(K))and characterizations of somefinite groups throughPrg(H,Aut(K)).
📌 3 Key Takeaways
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Objective & Hypothesis:LetH⊆Kbe two subgroups of a finite groupGandAut(K)the automorphism groupofK.
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Key Findings & Data:In this paper, we consider the generalized autocommuting probability ofGrelativeto its subgroupsHandK, denoted byPrg(H,Aut(K)), which is the probability thatthe autocommutator of a randomly chosen pair of elements, one fromHand the otherfromAut(K), is equal to a given elementg∈K.
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Conclusion & Impact:As applications of the computingformulae, we also obtain several bounds forPrg(H,Aut(K))and characterizations of somefinite groups throughPrg(H,Aut(K)).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
LetH⊆Kbe two subgroups of a finite groupGandAut(K)the automorphism groupofK. In this paper, we consider the generalized autocommuting probability ofGrelativeto its subgroupsHandK, denoted byPrg(H,Aut(K)), which is the probability thatthe autocommutator of a randomly chosen pair of elements, one fromHand the otherfromAut(K), is equal to a given elementg∈K. We study several properties as well asobtain several computing formulae of this probability. As applications of the computingformulae, we also obtain several bounds forPrg(H,Aut(K))and characterizations of somefinite groups throughPrg(H,Aut(K)).
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Cite This Article
DUTTA, P., NATH, R. K. (2022). Generalized autocommuting probability of a finitegroup relative to its subgroups. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 389–398. https://ajindex.com/articles/529646
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