• Hemant Kalra

      Articles written in Proceedings – Mathematical Sciences

    • A Note on Conjugacy Classes of Finite Groups

      Hemant Kalra Deepak Gumber

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      Let 𝐺 be a finite group and let $x^G$ denote the conjugacy class of an element 𝑥 of 𝐺. We classify all finite groups 𝐺 in the following three cases: (i) Each non-trivial conjugacy class of 𝐺 together with the identity element 1 is a subgroup of 𝐺, (ii) union of any two distinct non-trivial conjugacy classes of 𝐺 together with 1 is a subgroup of 𝐺, and (iii) union of any three distinct non-trivial conjugacy classes of 𝐺 together with 1 is a subgroup of 𝐺.

    • Finite groups with specific number of cyclic subgroups

      HEMANT KALRA

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      We classify all finite groups having exactly $6$, $7$ or $8$ cyclic subgroups. This gives a partial answer to the open problem posed by $\rm{T\breve{a}rn\breve{a}uceanu}$ (Amer. Math. Mon. 122 (2015) 275-276). As a consequence of our results, we also obtain an important result concerning the converse of Lagrange's theorem.

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