Existence of genetic divergence, appropriate characterization of breeding lines for economically important traits and determining parents with favourable alleles is the crux of crop genetic improvement programmes. This study is the first report of unravelling genetics and potential of petaloid-type cytoplasmic male sterile (pt-CMS) lines in carrot. Ten pt-CMS lines were crossed with 10 inbreds in line × tester mating fashion to generate 100 testcross progenies. Nutritional profiling of the 100 testcrosses progenies along with 20 parental types was carried out for two consecutive years for eight important traits to identify superior combiners. The pooled analysis revealed that the carotenoid content in root is under the genetic control of major genes (oligogenic). The pooled analysis revealed less than unity value of σ2A/D and σgca2/σsca2 for majority of the traits depicting preponderance of non-additive gene effects. The pt-CMS lines KT-28A, Kt-62A, KT-80A and KT-95A were identified as good combiners for carotenoids. The cross combination, KT-98A × KS-50 identified as the best heterotic combiner for CUPRAC and FRAP content over the years. Similarly, the combinations, KT-62A × KS-21, KT-80A × New Kuroda and KT-62A × KS-59 were found promising across the years for developing nutritionally rich F1 hybrids. The interaction analysis among the different antioxidant traits and plant pigments unveiled the scope of simultaneous improvement.

Let G be a finite group acting freely on a finitistic space X having cohomology type (0, b) (for example, $\mathbb S$n × $\mathbb S$2n is a space of type (0, 1) and the one-point union $\mathbb S$n ∨ $\mathbb S$2n ∨ $\mathbb S$3n is a space of type (0, 0)). It is known that a finite group G that contains ℤp ⊕ ℤp ⊕ ℤp, p a prime, cannot act freely on $\mathbb S$n × $\mathbb S$2n. In this paper, we show that if a finite group G acts freely on a space of type (0, 1), where n is odd, then G cannot contain ℤp ⊕ ℤp, p an odd prime. For spaces of cohomology type (0, 0), we show that every p-subgroup of G is either cyclic or a generalized quaternion group. Moreover, for n even, it is shown that ℤ2 is the only group that can act freely on X.