Hemant Kalra

activity

20112018

most citedFinite p-groups with central automorphism group of minimal order

7 citations · 8 across the 7 of their papers we have counts for

collaborators

9 papers

math.GR2018

Finite groups with specific number of cyclic subgroups

Hemant Kalra

In this note, we classify all finite groups having exactly 6, 7 or 8 cyclic subgroups. This gives a partial answer to the open problem posed by Tarnauceanu (Amer. Math. Monthly, 12…

math.GR2018

On the non-inner automorphism conjecture of finite $p$ -groups

Sandeep Singh, Hemant Kalra, Rohit Garg

A long-standing conjecture asserts that every finite non-abelian $p$ -group has a non-inner automorphism of order $p$ . In this paper, we settle the conjecture for a finite $p$ -group…

math.GR2018

On automorphisms of finite $p$ -groups

Hemant Kalra, Deepak Gumber

It is proved in [J. Group Theory, {\bf 10} (2007), 859-866] that if $G$ is a finite $p$ -group such that $(G, Z (G))$ is a Camina pair, then $∣ G ∣$ divides $|\Aut(G)|$. We give a very…

math.GR2014

Equality of certain automorphism groups of finite $p$ -groups

Deepak Gumber, Hemant Kalra

Let $G$ be a finite $p$ -group and let Aut $(G)$ denote the full automorphism group of $G$ . In the recent past, there has been interest in finding necessary and sufficient conditions…

math.GR2014

The conjugacy class number k(G) - a different perspective

Deepak Gumber, Hemant Kalra

Let $G$ be a finite group. Let $k (G)$ denote the number of conjugacy classes of $G$ and let $m (G)$ denote the least positive integer $n$ such that the union of any $n$ distinct non…

math.GR2013★ 7 cited

Finite p-groups with central automorphism group of minimal order

Deepak Gumber, Hemant Kalra

We study finite p-groups G of coclass upto 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…

math.GR2013★ 1 cited

Automorphisms of groups and converse of Schur's theorem

Deepak Gumber, Hemant Kalra, Sandeep Singh

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…

math.GR2011

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

Deepak Gumber, Hemant Kalra

Let $G$ be a finite non-abelian $p$ -group, where $p$ is a prime. Let $Aut_{c} (G)$ and $Aut_{z} (G)$ respectively denote the group of all class preserving and central a…

math.GR2011

On class preserving automorphisms of groups of order 32

Deepak Gumber, Hemant Kalra

We study class preserving automorphisms of groups of order thirty two and prove that only two groups have non-inner class preserving automorphisms.

Finite groups with specific number of cyclic subgroups

On the non-inner automorphism conjecture of finite p-groups

On automorphisms of finite p-groups

Equality of certain automorphism groups of finite p-groups

The conjugacy class number k(G) - a different perspective

Finite p-groups with central automorphism group of minimal order

Automorphisms of groups and converse of Schur's theorem

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

On class preserving automorphisms of groups of order 32

On the non-inner automorphism conjecture of finite $p$ -groups

On automorphisms of finite $p$ -groups

Equality of certain automorphism groups of finite $p$ -groups