Коллоквиум. Wondering About Sporadic Simple Groups

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In this talk, we begin with a brief description of the finite simple groups. The sporadic groups are finite simple groups not in one of the traditional infinite families, such as alternating groups, orthogonal groups over finite fields, etc. Five Mathieu groups were discovered in the 19th century and the remaining 21 were discovered in the period 1965 to 1975. Placement of the 26 sporadic groups in mathematics is still puzzling. We shall discuss thoughts about the sporadic groups from long past moments and recent times.