Meenakshi, and  Pooja Devi,
Maximal Subgroups of the Multiplicative Semigroup of $2\times 2$ Supertropical Matrices,
Indian Journal of Mathematics,
Volume 67,
Issue 02,
2025,
Pages 221--252,
ISSN 0019-5324,
Abstract:We give a complete characterisation of Green’s relations $\mathscr{L},\mathscr{R},\mathscr{H}$, $\mathscr{D}$ and $\mathscr{J}$ in the multiplicative semigroup of $2\times 2$ supertropical matrices. We determine the maximal subgroups of the semigroup $M_2(\mathbb{T})$ by finding the $\mathscr{R}- classes$ containing idempotents, followed by the identification of $\mathscr{H}- classes$.
Keywords: Supertropical algebra, Semigroup, Maximal subgroup.