Lifting Automorphisms of Quotients by Central Subgroups

2013/04/16 by Kane, Ben, Shallue, Andrew
#20F28 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1304.4632

Abstract

Given a finitely presented group G, we wish to explore the conditions under which automorphisms of quotients G/N can be lifted to automorphisms of G. We discover that in the case where N is a central subgroup of G, the question of lifting can be reduced to solving a certain matrix equation. We then use the techniques developed to show that Inn(G) is not characteristic in Aut(G), where G is a metacyclic group of order pⁿ, p≠ 2.

Related

• On equality of inner and absolute central automorphisms
• On central automorphisms of groups and nilpotent rings
• The Automorphism Group of p-Central p-Groups
• Lifting finite groups of outer automorphisms of free groups, surface groups and their abelianizations
• Finite p-groups with minimum number of central automorphisms fixing\n the center element-wise