If we wanted to show that two different groups (remember a group is a set with an operation) are essentially the same, we would have to have some way of connecting them to demonstrate that they really do match up and that the elements interact in the same way. Mathematicians have used these kinds of mappings to link groups so that we can show the structure is the same. a.) How would “linking” the two groups using a mapping help us show that the groups were structurally the same? b.)What key things would we want to “connect?” c.)To answer this, think about the important aspects of group structure. What would you connect to show those aspects are the same for two different groups?
If we wanted to show that two different groups (remember a group is a set with an operation) are essentially the same, we would have to have some way of connecting them to demonstrate that they really do match up and that the elements interact in the same way. Mathematicians have used these kinds of mappings to link groups so that we can show the structure is the same.
a.) How would “linking” the two groups using a mapping help us show that the groups were structurally the same?
b.)What key things would we want to “connect?”
c.)To answer this, think about the important aspects of group structure. What would you connect to show those aspects are the same for two different groups?
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