Strongly reversible classes in $\mathrm{SL}(n,\mathbb{C})$

Krishnendu Gongopadhyay; Tejbir Lohan; Chandan Maity

Strongly reversible classes in $\mathrm{SL}(n,\mathbb{C})$

Group Theory 2025-03-07 v2

Authors: Krishnendu Gongopadhyay , Tejbir Lohan , Chandan Maity

Abstract

An element of a group is called $\textit{strongly reversible}$ or $\textit{strongly real}$ if it can be expressed as a product of two involutions. We provide necessary and sufficient conditions for an element of $\mathrm{SL}(n,\mathbb{C})$ to be a product of two involutions. In particular, we classify the strongly reversible conjugacy classes in $\mathrm{SL}(n,\mathbb{C})$ .

Keywords

conjugacy classes in groups finite group theory wreath product of groups

Cite

@article{arxiv.2307.07967,
  title  = {Strongly reversible classes in $\mathrm{SL}(n,\mathbb{C})$},
  author = {Krishnendu Gongopadhyay and Tejbir Lohan and Chandan Maity},
  journal= {arXiv preprint arXiv:2307.07967},
  year   = {2025}
}

Comments

Final version (26 pages), incorporating revisions to the title, abstract, and statement of the main result from the earlier draft; to appear in the Proceedings of the Edinburgh Mathematical Society

Strongly reversible classes in $\mathrm{SL}(n,\mathbb{C})$

Abstract

Keywords

Cite

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