On mennicke groups of deficiency zero I

On the Structure of Some Deficiency Zero Groups

Groups of deficiency zero

We make a systematic study of groups of deeciency zero, concentrating on groups of prime-power order. We prove that a number of p-groups have deeciency zero and give explicit balanced presentations for them. This signiicantly increases the number of such groups known. We describe a reasonably general computational approach which leads to these results. We also list some other nite groups of dee...

on the structure of some deficiency zero groups

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From Mennicke symbols to Euler class groups

Bhatwadekar and Raja Sridharan have constructed a homomorphism from an orbit set of unimodular rows to an Euler class group. We show under weaker assumptions that a generalization of its kernel is a subgroup. Our tool is a partially defined operation on the set of unimodular matrices with two rows. 1 The exact sequence Consider a commutative noetherian Q-algebra A of dimension d. Let n = d + 1....

On Zero-sum Partitions of Abelian Groups

In this paper, confirming a conjecture of Kaplan et al., we prove that every abelian group G, which is of odd order or contains exactly three involutions, has the zerosum-partition property. As a corollary, every tree with |G| vertices and at most one vertex of degree 2 is G-anti-magic.