Mathematik-Online problems: Problem 521: Operation Table, Axioms of Groups

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	Mathematik-Online problems:
	Problem 521: Operation Table, Axioms of Groups

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Let

be the set of all prime numbers $\leq 13$ . Define on

the binary operation $\diamond: P\times P \longrightarrow P$ , with

$\displaystyle p \diamond q =$ greatest prime factor of $\displaystyle p+q-2 \; ,$

a): Calculate the operation table of $(P,\diamond)$ .
b): Find a solution of $5\diamond x=5$ in $(P,\diamond)$ , and indicate whether $(P,\diamond)$ is a group or not.

(Authors: Höllig/Höfert)

automatisch erstellt am 14. 10. 2004