research

# On the Exponent Conjectures

## Abstract

If \$p\$ is an odd prime, then we prove that \$\e(H_2(G,\mathbb{Z})) \mid p\ \e(G)\$ for \$p\$ groups of class 7. We prove the same for \$p\$ groups of class at most \$p+1\$ with \$\e(Z(G))=p\$. We also prove Schurs conjecture if \$\e(G/Z(G))\$ is \$2,3\$ or \$6\$. Furthermore we prove that if \$G\$ is a solvable group of derived length \$d\$ and \$\e(G)=p\$, then \$\e(H_2(G,\mathbb{Z})) \mid (\e(G))^{d-1}\$. We also show that if \$G\$ is a finite \$2\$ or \$3\$ generator group of exponent 5, then \$\e(H_2(G,\mathbb{Z})) \mid (\e(G))^2\$.Comment: 22 pages, Preliminary/second Draft Versio

## Similar works

This paper was published in arXiv.org e-Print Archive.

# Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.