Capable Two-generator 2-groups of Class Two
نویسنده
چکیده
A group is called capable if it is a central factor group. We characterize the capable 2-generator 2-groups of class 2 in terms of a standard presentation.
منابع مشابه
nth-roots and n-centrality of finite 2-generator p-groups of nilpotency class 2
Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.
متن کاملGenerator 2 - Groups of Class Two
A group is called capable if it is a central factor group. We characterize the capable 2-generator 2-groups of class 2 in terms of a standard presentation.
متن کاملCertain homological functors of 2 - generator p - groups of class 2
Using a new classification of 2-generator p-groups of class 2, we compute various homological functors for these groups. These functors include the nonabelian tensor square, nonabelian exterior square and the Schur multiplier. We also determine which of these groups are capable and which are unicentral.
متن کاملCapable Groups of Prime Exponent and Class Two Ii
We consider the capability of p-groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition based on the ranks of G/Z(G) and [G, G].
متن کاملSome Results on Capable Groups of Prime Exponent and Class Two
This note collects several results on the capability of p-groups of class two and prime exponent. Among our results, we settle the 4-generator case for this class. Introduction. In this note we collect sundry results related to the capability of finite p-groups of class two and prime exponent, using the approach introduced in [6]. We restrict to odd primes, since the case of abelian groups is w...
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تاریخ انتشار 2004