Contents of node6

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<H1><A ID="SECTION00030000000000000000"> Roman type</A> </H1>

Numbers, punctuation, (parentheses), [brackets], braces, and symbols used as tags should always be set in roman type. The following sample theorem illustrates how to code for roman type within the statement of a theorem.

<DIV>Theorem 3.1   Let <IMG STYLE="" SRC="img4.png" ALT=" $\cal {G}$ "> be a free nilpotent-of-class-2 group of rank ≥2 with carrier G and let <!– MATH

m : G×G→Z

–> <DIV ALIGN="CENTER"> m : G×G→Z </DIV> satisfy (2.21), (2.22), and (2.24), and define κ by (2.23). Then this kappa-group is kappa-nilpotent of class 2 and kappa-metabelian, that is to say, it satisfies S2 and S3, but it is kappa-abelian if, and only if, <DIV ALIGN="CENTER"> <!– MATH

m(x, y) = - 1 for all x, y $\notin$ G'.

(1)

–> <TABLE WIDTH="100<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP> m(x, y) = - 1    for all <!– MATH x, y $\notin$ G' –> x, y <IMG STYLE="" SRC="img5.png" ALT=" $\notin$ ">G'. </TD> <TD WIDTH=10 ALIGN="RIGHT"> (3.1)</TD></TR> </TABLE> </DIV> (Thus (3.1) implies the trivial consequence (2.1).) Assume now that (3.1) does not hold, so that the kappa-group is kappa-nonabelian. Assume further that m is not constant outside G' (inside G' the values of m clearly do not matter). Then κ is neither left nor right linear, that is to say, neither S4 nor S5 holds: I1 again holds, but none of I2–I5. As before, I6 is equivalent to (2.25). Now I7', however, is equivalent to a condition similar to (2.25), namely <DIV ALIGN="CENTER"> <!– MATH

m(xzσ, yzσ) = m(x, y) .

(2)

–> <TABLE WIDTH="100<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP> m(xzσ, yzσ) = m(x, y) . </TD> <TD WIDTH=10 ALIGN="RIGHT"> (3.2)</TD></TR> </TABLE> </DIV></DIV>

Letters used as abbreviations rather than as variables or constants are set in roman type. Use the control sequences [<A HREF="node12_ct.html#spivak:jot" TARGET="contents">12</A>, p. 95] for common mathematical functions and operators like log and lim, and use <code>[#!cite!#]</code> when citing a reference. The reference tag will be bold automatically, but you will need to set any additional information in roman type as illustrated by the coding of the previous sentence.

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