Abstract
Let S be a set. A map**
is sometimes called a law of composition (of S into itself). If x, y are elements of S, the image of the pair (x, y) under this map** is also called their product under the law of composition, and will be denoted by xy. (Sometimes, we also write x ยท y, and in many cases it is also convenient to use an additive notation, and thus to write x + y. In that case, we call this element the sum of x and y. It is customary to use the notation x + y only when the relation x + y = y + x holds.)
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Bibliography
D. Gorenstein, Finite groups, Harper and Row, 1968
D. Gorenstein, Finite simple groups, Plenum Press, 1982
D. Gorenstein, The Classification of Finite Simple Groups, Plenum Press, 1983
D. Gorenstein, Classifying the finite simple groups, Bull. AMS 14 No. 1 (1986), pp. 1โ98
R. Solomon, A brief history of the classification of the finite simple groups, Bull. AMS 38,3 (2001) pp. 315โ352
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ยฉ 2002 Springer Science+Business Media New York
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Lang, S. (2002). Groups. In: Algebra. Graduate Texts in Mathematics, vol 211. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0041-0_1
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DOI: https://doi.org/10.1007/978-1-4613-0041-0_1
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