Groups of order $p^m$ containing exactly $p + 1$ abelian subgroups of order $p^{m - 1}$
نویسندگان
چکیده
منابع مشابه
THE GROUPS OF ORDER pm WHICH CONTAIN EXACTLY p CYCLIC SUBGROUPS OF ORDER
If a group ( G ) of order pm contains only one subgroup of order pa, a > 0, it is known to be cyclic unless both p = 2 and at = l.f In this special case there are two possible groups whenever m > 2. The number of cyclic subgroups of order pa in G is divisible by p whenever G is non-cyclic and p > 2. J In the present paper we shall consider the possible types of G when it is assumed that there a...
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It would be interesting to extend this result by allowing B to have nilpotence class 2 instead of necessarily being abelian. This cannot be done if p = 2 (Example 4.2), but perhaps it is possible for p odd. (It was done by the author ([Gor, p.274]; [HB, III, p.21]) for the special case in which p is odd and [B,B] ≤ A.) However, there is an application of Thompson’s Replacement Theorem that can ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1907
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1907-01435-0