Examples and Properties
- The elementary abelian group (Z/2Z)2 has four elements: { (0,0), (0,1), (1,0), (1,1) }. Addition is performed componentwise, taking the result mod 2. For instance, (1,0) + (1,1) = (0,1).
- (Z/pZ)n is generated by n elements, and n is the least possible number of generators. In particular, the set {e1, ..., en}, where ei has a 1 in the ith component and 0 elsewhere, is a minimal generating set.
- Every elementary abelian group has a fairly simple finite presentation.
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- (Z/pZ)n < e1, ..., en | eip = 1, eiej = ejei >
Read more about this topic: Elementary Abelian Group
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“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)