The Schur multiplicator of metacyclic groups

Beyl, F. Rudolf

doi:10.1090/s0002-9939-1973-0325759-7

Cited by 24 publications

(10 citation statements)

References 6 publications

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“…This settles the corresponding statements in (1) and (4). The proof of the remaining statements is again straightforward and left to the reader.…”

Section: (H) (!) = (!)Asusualsupporting

confidence: 74%

Cohomology of Metacyclic Groups

Huebschmann¹

1991

Transactions of the American Mathematical Society

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Abstract. Let e: 1 -> N -► G -► K -> 1 be an extension of a finite cyclic group N by a finite cyclic group K . Using homological perturbation theory, we introduce the beginning of a free resolution of the integers Z over the group ring ZG of G in such a way that the resolution reflects the structure of G as an extension of N by K, and we use this resolution to compute the additive structure of the integral cohomology of G in many cases. We proceed by first establishing a number of special cases, thereafter constructing suitable cohomology classes thereby obtaining a lower bound, then computing characteristic classes introduced in an earlier paper, and, finally, exploiting these classes, obtaining upper bounds for the cohomology via the integral cohomology spectral sequence of the extension e. The calculation is then completed by comparing the two bounds.

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“…This settles the corresponding statements in (1) and (4). The proof of the remaining statements is again straightforward and left to the reader.…”

Section: (H) (!) = (!)Asusualsupporting

confidence: 74%

Cohomology of Metacyclic Groups

Huebschmann¹

1991

Transactions of the American Mathematical Society

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“…THEOREM 2. Suppose that The fact that (ar) n s 1 mod a In now shows that the results of Beyl (1973) are applicable to F(r, n, k, s) when r, n, k and s satisfy conditions (i), (ii) and (iii) and so it may be presented in the form ia,b\a aln = l,b~1ab = a<* r , b n = a* Mr -*>>.…”

Section: A Standard Metacyclic Schur Group Presentationmentioning

confidence: 98%

Finitely presented groups of Fibonacci type. part II

Campbell

Robertson

1979

J. Aust. Math. Soc.

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“…Finite metacyclic groups are efficient. This was shown by Beyl [6] and Wamsley [27]. Infinite metacyclic groups, however, need not be efficient, a result due to Baik and Pride [5] (see also [3]).…”

Section: We Say G Is Efficient If Def (G) = 5(g) and A Presentation mentioning

confidence: 99%