Glasnik Matematicki, Vol. 43, No.1 (2008), 59-95.

ON THE NUMBER OF SUBGROUPS OF GIVEN TYPE IN A FINITE p-GROUP

Yakov Berkovich

Abstract.   We study the p-groups G containing exactly p+1 subgroups of order p^p and exponent p. A number of counting theorems and results on subgroups of maximal class and p-groups with few subgroups of given type are also proved. Counting theorems play crucial role in the whole paper.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   p-groups of maximal class, regular and absolutely regular p-groups.

DOI: 10.3336/gm.43.1.06

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