Questions tagged [cayley-table]

For questions about Cayley tables, a table that describes the structure of a finite group by arranging all the possible products of all the group's elements in a square table reminiscent of an addition or multiplication table.

A Cayley table, after the 19th century British mathematician Arthur Cayley, describes the structure of a finite group by arranging all the possible products of all the group's elements in a square table reminiscent of an addition or multiplication table. Many properties of a group — such as whether or not it is abelian, which elements are inverses of which elements, and the size and contents of the group's center — can be discovered from its Cayley table.

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Unable to understand how six substitutions (functions) form a group.

Have a doubt in exercise that is repeated in two texts (as stated at the end)- Suppose there are six elements $1,a,b,c,d,e$ whose laws of combination are given by the table. As per the table, there is identity and inverse; with implied closure…
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