Roman type

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.

Theorem 3.1   Let be a free nilpotent-of-class-2 group of rank ≥2 with carrier G and let

m : G×G→Z

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,

m(x, y) = - 1    for all x, y G'.

(3.1)

(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

m(xzσ, yzσ) = m(x, y) .

(3.2)

Letters used as abbreviations rather than as variables or constants are set in roman type. Use the control sequences [12, p. 95] for common mathematical functions and operators like log and lim, and use \cite 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.