# nt.quantity concept – On the variety of construction of Fp[G]-modules Answer

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## nt.quantity concept – On the variety of construction of Fp[G]-modules

There is a sizable variety of discrete (as much as module isomorphism) $${mathbb F}_pG$$-modules, plane in diminutive dimensions, and I do not cerebrate you’ll be able to await for any kindly of affordable classification.

I did some brisk pc calculations.
For $$p=2$$, the variety of isomorphism courses of dimensions 1,2, …, 7 is 1, 5, 11, 28, 53, 111, 199.

For $$p=3$$ in dimensions 1,2,3,4,5, it’s 1,6, 25, 78, 235.

For $$p=5$$ in dimensions 1,2,3,4, it’s 1,8,47,310.

Of passage, it’s adequate to categorise the indecomposable modules, however $${mathbb F}_pG$$ is of so-called wild illustration kind, which suggests kind of that this can’t simply breathe carried out!

For instance, with $$p=5$$ in dimension 4, 242 of the 310 modules are indecomposable.

On the opposite hand, I’m under no circumstances an skilled in modular illustration concept, and it’s workable that extra can breathe stated.

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