✨
AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this work, the group Aut C ( ℤ 3² ⋊ ϕ ℤ₃ ) of all central automorphisms of ℤ 3² ⋊ ϕ ℤ₃ is studied and we determine the form of central automorphisms of ℤ 3² ⋊ ϕ ℤ 3 .
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Let ℤ p² ⋊ ϕ ℤ p be the semi-direct product of ℤ p² and ℤ p with respect to ϕ, (ϕ is homomorphism from ℤ p to automorphisms group of ℤ p² ).
📊
Key Findings & Data:Let ℤ p² ⋊ ϕ ℤ p be the semi-direct product of ℤ p² and ℤ p with respect to ϕ, (ϕ is homomorphism from ℤ p to automorphisms group of ℤ p² ).
💡
Conclusion & Impact:In this work, the group Aut C ( ℤ 3² ⋊ ϕ ℤ₃ ) of all central automorphisms of ℤ 3² ⋊ ϕ ℤ₃ is studied and we determine the form of central automorphisms of ℤ 3² ⋊ ϕ ℤ 3 .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:P-group · Semi-direct product
Abstract
Let ℤ p² ⋊ ϕ ℤ p be the semi-direct product of ℤ p² and ℤ p with respect to ϕ, (ϕ is homomorphism from ℤ p to automorphisms group of ℤ p² ). In this work, the group Aut C ( ℤ 3² ⋊ ϕ ℤ₃ ) of all central automorphisms of ℤ 3² ⋊ ϕ ℤ₃ is studied and we determine the form of central automorphisms of ℤ 3² ⋊ ϕ ℤ 3 .
Keywords
🔖
Cite This Article
Oztekın, O., Gurbuz, Z. (2018). Central Automorphism Groups for Semidirect Product of p-Groups. The Eurasia Proceedings of Science Technology Engineering and Mathematics, Issue: 2. https://ajindex.com/articles/1551599