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# Tag Archives: elements

## MaBloWriMo 19: groups from monoids

So, you have a monoid, that is, a set with an associative binary operation that has an identity element. But not all elements have inverses, so it is not a group. Assuming you really want a group, what can you … Continue reading

Posted in algebra, group theory, proof
Tagged elements, groups, inverses, MaBloWriMo, monoids, proof
1 Comment

## MaBloWriMo 15: One more fact about element orders

I almost forgot, but there is one more fact about the order of elements in a group that we will need. Suppose we have some and we happen to know that is the identity. What can we say about the … Continue reading

Posted in algebra, group theory, number theory, proof
Tagged elements, finite, groups, MaBloWriMo, order
1 Comment

## MaBloWriMo 14: Element orders are no greater than group size

Today we will give an answer to the question: What is the relationship between the order of a group and the orders of its elements? Yesterday, I claimed we would prove that for any element of a group , it … Continue reading

Posted in algebra, group theory, proof
Tagged elements, finite, groups, MaBloWriMo, order
2 Comments

## MaBloWriMo 13: Elements of finite groups have an order

Recall from yesterday that if is a group and is some element of the group, the order of is defined as the smallest number of copies of which combine to yield the identity element. I forgot to mention it yesterday, … Continue reading

Posted in algebra, group theory, proof
Tagged elements, finite, groups, MaBloWriMo, order