# Paper “A note on normal complements for finite groups” published in Bull. Austral. Math. Soc.

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Ning Su, Adolfo Ballester-Bolinches, Hangyang Meng.

A note on normal complements for finite groups

Bull. Austral. Math. Soc., 98 (1):109-112, 2018

doi:10.1017/S0004972718000151

Abstract

Assume that G is a finite group and H is a 2-nilpotent Sylow tower Hall subgroup of G such that if x and y are G-conjugate elements of H ∩ G0 of prime order or order 4, then x and y are H-conjugate. We prove hat there exists a normal subgroup N of G such that G = HN and H ∩ N = 1.

2010 Mathematics Subject Classification: primary 20D20; secondary 20D10

Keywords: finite group, conjugation, Hall subgroup, normal complement.

# Paper “Finite trifactorised groups and $\pi$-decomposability” published in Bull. Austral. Math. Soc.

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L. S. Kazarin, A. Martínez-Pastor, M. D. Pérez-Ramos.

Finite trifactorised groups and $\pi$-decomposability

Bull. Austral. Math. Soc., 97 (2):218-228, 2018

doi:10.1017/S0004972717001034

Abstract

We derive some structural properties of a trifactorised finite group G = AB = AC = BC, where A, B, and C are subgroups of G, provided that A = Aπ × Aπ’ and B = Bπ × Bπ’ are π-decomposable groups, for a set of primes π.

2010 Mathematics Subject Classification: primary 20D40; secondary 20D20

Keywords: finite group, product of subgroups, π-decomposable group, π-structure.

# Paper “On a theorem of Kang and Liu on factorised groups” published in Bull. Austral. Math. Soc.

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A. Ballester-Bolinches, M. C. Pedraza Aguilera

On a theorem of Kang and Liu on factorised groups

Bull. Austral. Math. Soc., 97 (1):54-56, 2018

https://doi.org/10.1017/S0004972717000363

Abstract

Kang and Liu [‘On supersolvability of factorized finite groups’, Bull. Math. Sci. 3 (2013), 205–210] investigate the structure of finite groups that are products of two supersoluble groups. The goal of this note is to give a correct proof of their main theorem.

2010 Mathematics Subject Classification: primary: 20D10, secondary: 20D20, 20D40

Keywords: finite group. factorisation, supersolubility

# Paper “On conjugacy of supplements of normal subgroups of finite groups” published in Bull. Austral. Math. Soc.

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A. Ballester-Bolinches, L. M. Ezquerro

On conjugacy of supplements of normal subgroups of finite groups

Bull. Aust. Math. Soc., 89 (2014), 293–299

http://dx.doi.org/10.1017/S0004972713000506

Abstract

The objective of this paper is to find some sufficient conditions to ensure the conjugacy of supplements of a normal subgroup of a soluble group.

2010 Mathematics subject classification: primary 20D10; secondary 20D15, 20D20

Keywords and phrasesfinite groups, supplements, Schunck classes, formations