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On the Number of Subgroups of Given order and Exponent p in a Finite Irregular p ‐Group
Author(s) -
Berkovich Yakov
Publication year - 1992
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/24.3.259
Subject(s) - mathematics , exponent , order (exchange) , combinatorics , integer (computer science) , group (periodic table) , class (philosophy) , physics , philosophy , linguistics , finance , quantum mechanics , artificial intelligence , computer science , economics , programming language
If G is a p ‐group of order p m and exponent p , m > 3, n ε{2,…, m − 2}, then [1] G contains 1+ p +2 p 2 + kp 2 ( k ⩾ 0 is an integer) subgroups of order p n . In this note we prove an analogous result for irregular p ‐groups, p > 3, which are not groups of maximal class for n ε{2,…, p −2}.
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