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Algebra Letters
Number of Followers: 1

This is an Open Access Journal

Open Access journal
ISSN (Print) 2051-5502
Published by Science and Knowledge Publishing Corporation Limited

[5 journals]

Generalized order divisor graphs associated with finite groups
- Authors: Shafiq ur Rehman, Muhammad Imran, Sehrish Bibi, Rubab Gull
  Abstract: For each finite group G we associate a simple graph Ω(G). We investigate the coaction between the group-theoretic properties of G and the graph-theoretic properties of Ω(G).
  PubDate: 2022-09-19
  Issue No: Vol. 2022 (2022)
On a non-solvable group satisfying xG=(x−1)G
- Authors: Shiv Narain
  Abstract: A group G satisfies Syskin’s condition if elements of same order are conjugates. If a group G satisfies Syskin’s condition, then each element and its inverse are conjugate to each other, i.e., for all x∈G, xG=(x−1)G, but not conversely. Thus, the class of those groups satisfying Syskin’s condition forms a proper subclass of groups satisfying xG=(x−1)G. In this note, it is proved that if a group G meets the condition xG=(x−1)G, then G cannot be of odd order. As the main result, it is shown that if xG=(x−1)G holds for a centreless and non-solvable group G of order 120 such that G≠G’, then G≌S5.
  
  PubDate: 2022-09-08
  Issue No: Vol. 2022 (2022)

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