Description:
Definitions for forms Form 227 and Form 228.
Content:
Definitions for forms Form 227 and Form 228.
Definition:
- A partially ordered group is a triple \((G,\circ,\le)\) such that \((G,\circ )\) is a group and \((G,\le )\) is a partially ordered set satisfying for all \(x,\ y,\ a\) and \(b\) in \(G\) if \(x\le y\),then \(axb\le ayb\).
- \(P = \{a\in G: a\ge e\}\) is the positive cone (where \(e\) is the identity in \(G\)).
- If \(P\cup P^{-1} = G\) then \(G\) is fully ordered. (This is equivalent to saying that \(\le\) is a linear ordering.)
- A group is torsion free if the only element of finite order is the identity element.
Howard-Rubin number:
79
Type:
Definitions
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