Finite p-Groups up to Isoclinism, Which Have Only Two Conjugacy Lengths
نویسندگان
چکیده
منابع مشابه
Finite Groups Have More Conjugacy Classes
We prove that for every > 0 there exists a δ > 0 so that every group of order n ≥ 3 has at least δ log2 n/(log2 log2 n) 3+ conjugacy classes. This sharpens earlier results of Pyber and Keller. Bertram speculates whether it is true that every finite group of order n has more than log3 n conjugacy classes. We answer Bertram’s question in the affirmative for groups with a trivial solvable radical.
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Of course, in that problem we have to take into account that the class sizes impose restrictions on the group structure. E.g. if the sizes are {1, p}, then the nilpotency class has to be 2. More precisely: the class sizes of a p-group G are {1, p} iff |G′| = p (Knoche; see also Theorem 3 below). But we can ask, e.g., if, given any set S ≠ {1, p} of p-powers, does there exist a group of class 3 ...
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In this paper we classify finite groups whose nonnormal subgroups are of order p or pq, where p, q are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.
متن کاملFinite Groups Have Even More Conjugacy Classes * By
In his paper ”Finite groups have many conjugacy classes” (J. London Math. Soc (2) 46 (1992), 239-249), L. Pyber proved the to date best general lower bounds for the number of conjugacy classes of a finite group in terms of the order of the group. In this paper we strengthen the main results in Pyber’s paper.
متن کاملON THE NUMBER OF CONJUGACY CLASSES OF FINITE p-GROUPS
Denote k(G) the number of conjugacy classes of a group G. Some inequalities are deduced by arithmetic means for k(G), where G is a p-group. As an application, k(G) is calculated for special cases of p-groups. A method of estimating k(G) for some finite groups, others then p-groups is also presented.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7907