KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Algebra / 2023 / Cilt: 34 Sayı: 34

A note on Friendly and Solitary Groups

Shubham MITTAL
Gaurav MITTAL
R. K. SHARMA
Sayfa
197–206
Yayın Tarihi
2023-07-10
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We provide many examples of friendly and solitary groups and study certain properties of the type-2 friends of cyclic $p$-groups, where $p$ is a prime number.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we extend the notions of friendly and solitary numbers to group theory and define friendly and solitary groups of type-1 and type-2.
📊
Temel Bulgular & Veri:In this paper, we extend the notions of friendly and solitary numbers to group theory and define friendly and solitary groups of type-1 and type-2.
💡
Sonuç & Katkı:We provide many examples of friendly and solitary groups and study certain properties of the type-2 friends of cyclic $p$-groups, where $p$ is a prime number.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Group · $p$-group · number theory

Abstract

In this paper, we extend the notions of friendly and solitary numbers to group theory and define friendly and solitary groups of type-1 and type-2. We provide many examples of friendly and solitary groups and study certain properties of the type-2 friends of cyclic $p$-groups, where $p$ is a prime number.

🔖

Bu Makaleye Atıf Yap

MITTAL, S., MITTAL, G., SHARMA, R. K. (2023). A note on Friendly and Solitary Groups. International Electronic Journal of Algebra, Cilt: 34 Sayı: 34, 197–206. https://ajindex.com/articles/953324

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (12)

  1. C. W. Anderson, D. Hickerson and M. Greening, Problems and Solutions: Solutions of Advanced Problems: 6020, Friendly integers, Amer. Math. Monthly, 84(1) (1977), 65-66.
  2. W. Burnside, On groups of order $p^{\alpha}q^{\beta}$ (Second Paper), Proc. London Math.Soc., 2(2) (1905), 432-437. J. Cemra, 10 Solitary check, Github/CemraJC/Solidarity. W. Feit and J. G. Thompson, Solvability of groups of odd order, Pacific J.Math., 13 (1963), 775-1029.
  3. J. Gallian, Contemporary Abstract Algebra, Chapman and Hall/CRC, 2021.
  4. GAP-Groups, Algorithms, and Programming, version 4:12:0, gap-system.org, 2022.
  5. K. Guha and S. Ghosh, Measuring abundance with abundancy index, Ball State Undergraduate Math. Exch., 15(1) (2021), 28-39.
  6. J. Kirtland, Complementation of Normal Subgroups: in Finite Groups, De Gruyter, Berlin, 2017.
  7. T. Leinster, Perfect numbers and groups, arXiv:math/0104012, 2001.
  8. T. De Medts and A. Maroti, Perfect numbers and finite groups, Rend. Semin. Mat. Univ. Padova, 129 (2013), 17-33.
  9. C. P. Milies and S. K. Sehgal, An Introduction to Group Rings, Algebra and Applications, 1, Kluwer Academic Publishers, Dordrecht, 2002.
  10. G. Mittal and R. K. Sharma, On unit group of finite semisimple group algebrasof non-metabelian groups up to order 72, Math. Bohem., 146(4) (2021), 429-455.
  11. P. Pollack and C. Pomerance, Some properties of Erdos on the sum-of-divisors function, Trans. Amer. Math. Soc. Ser. B, 3 (2016), 1-26.
  12. M. Tarnauceanu, Finite groups determined by an inequality of the orders of their normal subgroups, An. Stiint. Univ. Al. I. Cuza Iai. Mat. (N.S.) 57(2) (2011), 229-238.