Sentence:  If \Delta is a finite group, its cardinality is called the <WSD>order</WSD> of \Delta. The <WSD>order</WSD> of an element a \in \Delta is defined as the smallest nonnegative integer n such that a^n = 1_\Delta. The second case of the following result is known as Cauchy's theorem. / Theorem 1.10 "Let \Delta be a finite group." / : "(i) The <WSD>order</WSD> of an element a \in \Delta divides the order |\Delta| of the group." / : "(ii) If a prime number p divides |\Delta|, then there exists an element a \in \Delta of <WSD>order</WSD> p." 
Meaning of the word marked with <WSD> tags:  For given group "G" and element "g" ∈ "G", the smallest positive natural number "n", if it exists, such that (using multiplicative notation), "gn = e", where "e" is the identity element of "G"; "if no such number exists, the element is said to be of '''infinite order''' (or sometimes '''zero order''')."