Glasnik Matematicki, Vol. 40, No.1 (2005), 51-58.
A PROPERTY OF GROUPS OF ORDER
≤ pp(e+1) AND EXPONENT pe
Yakov Berkovich
Department of Mathematics, University of Haifa,
Haifa 31905, Israel
e-mail: berkov@mathcs2.haifa.ac.il
Abstract. Let G be a p-group of exponent
pe and order
pm,
where m < p(e+1)
if p > 2 and m
≤ 2(e+1) if
p = 2. Then, if
e-1(G) is irregular,
then p = 2, e = 2 and
e-1(G)
D8 × C2, where
|C2| = 2 and D8 is dihedral of order 8.
2000 Mathematics Subject Classification.
20C15.
Key words and phrases. Pyramidal, regular, absolutely
regular, irregular and metacyclic p-groups,
p-groups of maximal class.
Full text (PDF) (free access)
DOI: 10.3336/gm.40.1.06
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