We collect a few examples as follows: For (k ge 2), in the space (mathcal{M }_k) of marked groups of rank (k): (i) "Being abelian" is both an open and a closed property; more generally, for (d ge 1), "being nilpotent of nilpotent class at most (d)" is both open and closed.
Then (d) is a metric (indeed an ultrametric) and makes the set (2^{F_k}) of subsets of (F_k) a totally discontinuous compact metric space, in which the space (mathcal{M }_k) of marked groups on (k) generators (namely the space of normal subgroups of (F_k)) is closed.
In F. gracilis and F. tibetica, 25S rDNA sites among three homologous chromosome groups were not of noticeably different signal intensities, while in F. corymbosa (CFRA 1911, Figure 3B), 25S rDNA sites in one "single-marked" group of four chromosomes had larger signals than those of the other two groups.
We denote by (mathcal{M }_k) the set of marked groups on (k) generators, identified here with the set of normal subgroups of (F_k) via the bijection ((G,S) longleftrightarrow ker pi _G).
With the notation above, we have begin{aligned} N, =, ker pi, quad text{ namely } quad G_0/N = G, end{aligned}so that begin{aligned} lim _{n rightarrow infty } G_n, =, G end{aligned}in the space of marked groups on (vert S vert ) generators (in the sense of Section 3).
We have begin{aligned} N_omega, =, ker left( pi _omega : G_0 longrightarrow G_omega right), quad text{ namely } G_omega simeq G_0/N_omega, end{aligned}so that begin{aligned} lim _{n rightarrow infty } G_{omega,n}, =, G_omega end{aligned}in the space of marked groups on (4) generators.
There were no marked group differences in levels of S100B, no major imbalance in the ratios of pro- to anti-inflammatory interleukins nor in the metabolism of kynurenine to toxic metabolites in ADHD.
At the time of interdisciplinary consultation, analysis of the mean age of patients disclosed marked group differences: 66.44 years in Cohort I vs. 69.31 years in Cohort II (p < .001).001
We will recall the construction of [68], which is a generalisation of that of Section 2. It associates with each point (omega in Omega ) a marked group ((G_omega,S_omega )) with (S_omega ) consisting of (4) generators of order (2); for example, (mathfrak{G } = G_{overline{012}}), where (overline{012}) stands for the (3 -periodic sequence (012012012cdots ).
The results indicated marked group differences in the magnitude of NK suppression by MP: EC 50 was 2.6-fold lower in the luteal phase compared to the follicular phase, and 1.8-fold lower in OC users compared to men, who were least susceptible to the effects of MP.
