Deepak Gumber

On Central Automorphisms of Finite p-Groups

We characterize all finite p-groups G of order p n (n ≤ 6), where p is a prime for n ≤ 5 and an odd prime for n = 6, such that the center of the inner automorphism group of G is equal to the group of central automorphisms of G.

Finite p-groups with Central Automorphism Group of Minimal Order

We study finite p-groups G of coclass up to 4 for which the group Aut z (G) of all central automorphisms of G is of minimal possible order. As a consequence, we obtain very short and elementary proofs of main results of Sharma and Gumber [7].

IA-automorphisms of finitely generated nilpotent groups

An automorphism of a group G is called an IA-automorphism if it induces the identity automorphism on the abelianized group G/G′. Let IA(G) denote the group of all IA-automorphisms of G. We classify all finitely generated nilpotent groups G of class 2 for which IA(G) ≃ Inn(G). In particular, we classify all finite nilpotent groups of class 2 for which each IA-automorphism is inner.

Equality of certain automorphism groups of finite p-groups

Let

Automorphism groups of finitely generated groups that are isomorphic to group of inner automorphisms

G

Some finite p-groups with central automorphism group of non-minimal order

be a finite

A note on commuting automorphisms of some finite p-groups

p

The Conjugacy Class Number k(G): A Different Perspective

-group and let Aut

On equality of central and class preserving automorphisms of finite p-groups

(G)

A note on conjugacy classes of finite groups

denote the full automorphism group of