Sentence:  In mathematics, <WSD>automorphisms</WSD> of algebraic structures play an important role. <WSD>Automorphisms</WSD> capture the symmetries inherent in the structures and many important results have been proved by analyzing the <WSD>automorphism</WSD> group of the structure. 
Meaning of the word marked with <WSD> tags:  An isomorphism of a mathematical object or system of objects onto itself.