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.
Volume 131, 2021
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