I'm trying to use DESeq2 to perform something like a one-way ANOVA on 3
groups of samples. I've seen the same question and answer here:

DESeq2 One-way ANOVA with 3 sample groups?

However, I can't seem to  get a single p value. I have my data input successfully, and I've been able to
perform pairwise comparisons using DESeq2 but I haven't been able to
extract one p-value across 3 different groups using Mike's kind reply code in the above post. Thanks for your help.

The code I used was 

group=factor(c("A","A","B","B","C","C"))
design(dds) = ~ group
dds = DESeq(dds, test = "LRT", reduced = ~ 1)
res=results(dds)

The still give the pairwise comparison, default C vs A p values. I can use contrast to get other pairwise p values but Is there anyway I can get a single p value per gene?

>sessionInfo()

R version 3.2.1 (2015-06-18)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 7 x64 (build 7601) Service Pack 1

locale:
[1] LC_COLLATE=English_United States.1252  LC_CTYPE=English_United States.1252    LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                           LC_TIME=English_United States.1252    

attached base packages:
[1] parallel  stats4    stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] ggplot2_1.0.1             gplots_2.17.0             RColorBrewer_1.1-2        limma_3.24.15             BiocInstaller_1.18.4     
 [6] DESeq2_1.8.1              RcppArmadillo_0.5.400.2.0 Rcpp_0.12.0               GenomicRanges_1.20.6      GenomeInfoDb_1.4.2       
[11] IRanges_2.2.7             S4Vectors_0.6.5           BiocGenerics_0.14.0      

"My question is, if I do res2=results(dds, contrast=c("condition", "B", "A")), I got another set of p values and LFC for B vs. A. same for C vs B."

I believe that you get a new LFC but the p-values should be exactly the same and they should say "LRT p-value...". Can you check this?

"This still gives the pairwise comparison, default C vs A p values"

No, the p-value here is for the comparison of the full model and the reduced model, so all 3 levels.

For the LRT, there is only one p-value per gene and it is the one you are getting back from results(). You will notice when you print the object that the LFC is associated with a comparison, but the p-value says "~condition" vs "~1". So is the visual indication to the user that the p-value is a LRT p-value, not a pairwise comparison of 2 levels. You can see either LFC by using the 'name' argument. But this doesn't change the fact that the p-value you see is associated with all 3 levels.

Please find the paragraph in the Details section in ?results about likelihood ratio test p-values.