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I will be happy if one gives references (oncluding current research) for `classification' (structure) of $p$-groups of maximal class which contain abelian maximal subgroup (i.e. abelian subgroup of index $p$).

I couldn't find the references online or in books of Y. Berkovich.

(Thanks in advance!)

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I believe the study of $p$-groups of maximal class really kicked off with this paper:

Blackburn, N. On a special class of p-groups. Acta Math. 100 1958 45–92.

These days the basic source is:

Leedham-Green, C. R.; McKay, Susan (2002), The structure of groups of prime power order, London Mathematical Society Monographs. New Series, 27, Oxford University Press.

If you can't get hold of these email me and I'll send you an e-copy.

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