- #1

cbarker1

Gold Member

MHB

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I am having some troubles with the problem. The problem states:

Let $(G,\star)$ be a group with ${a}_{1},{a}_{2},\dots, {a}_{n}$ in $G$. Prove using induction that the value of

${a}_{1}\star {a}_{2} \star \dots \star {a}_{n}$ is independent of how the expression is bracketed. My attempt

Base Case: We know that the definition of a group requires the associative property. So when $n=3$, associativity holds true.

Induction Hypothesis:

Assume $n>k$. (Here is where I am having troubles.)

Thanks,

Cbarker1