The phrase "a growing core" is correct and usable in written English.
It can be used to describe an increasing central element or group within a larger context, such as a business, community, or concept.
Example: "The organization has established a growing core of dedicated volunteers who are committed to its mission."
Alternatives: "an expanding center" or "a developing nucleus."
They can accomplish that in Iraq, where there are 145,000 American troops and a growing core of civilian administrators and experts.
There are a lot of larger cities with a growing core concentration of start-ups; 1871 in Chicago is co-working space in the Merchandise Mart that's become a hub of activity.
In the past few months, both Foursquare itself and a growing core of third-party developers have changed that.
Most big banks have an abysmal record of growing core deposits (total domestic bank deposits less domestic time deposits larger than $100,000).
To the growing core of ardent conservatives in the Senate, Mr. Cruz has offered a jolt of positive energy.
For the growing core models M14 to M17, the population core grew from an initial size of 104 individuals at 1,000 generations ago to 107 at present.
Upon dilution with water, LH dissolved in pH 4 solution formed growing cores and aggregated into nanoparticles, due to the maximum solubility of LH at pH 4.
These latter authors argued that the absence of a present-day magnetic field would be difficult to reconcile with a growing inner core and a chemical dynamo supporting inner-core growth would be difficult to stop in a continuously cooling planet.
In my own company, the main changes have been positive: a gradual increase in funding and audiences, and a growing organisational core supporting the company.
But what they do have, he said, is a relatively low cost of living, a growing urban core and "incredibly hospitable people and really decent people to be around".
Considering this contribution, sufficient power is indeed not available to drive a present-day dynamo, even with a growing inner core (Scheinberg et al. 2015).
