# Paper “Prime Power Indices in Factorised Groups” published in Mediterr. J. Math.

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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor

Prime power indices in factorised groups.

Mediterr. J. Math., 14(6):Art. 225, 15, 2017

https://doi.org/10.1007/s00605-016-0987-9

Abstract

Let the group G=AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in AB have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in AB have prime power indices in G. In particular, when G=A=B, we obtain as a consequence some known results.

2010 Mathematics Subject Classification: 20D10, 20D40, 20E45, 20D20

Keywords: Finite groups, Products of groups, Conjugacy classes, Sylow subgroups

# Paper “Square-free class sizes in products of groups” published in J. Algebra

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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor

Square-free class sizes in products of groups

J. Algebra, 491:190–206, 2017

https://doi.org/10.1016/j.jalgebra.2017.08.007

Abstract

We obtain some structural properties of a factorised group G=AB, given that the conjugacy class sizes of certain elements in AB are not divisible by , for some prime p. The case when G=AB is a mutually permutable product is especially considered.

2010 Mathematical Subject Classification: 20D10, 20D40, 20E45

Keywords: Finite groups, Soluble groups, Products of subgroups, Conjugacy classes

# Paper “On complements of F-residuals of finite groups” published in Comm. Algebra

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A. Ballester-Bolinches, S. F. Kamornikov, and V. Pérez-Calabuig

On Complements of F-residuals of finite groups

Comm. Algebra, 45(2):878–882, 2017.

https://doi.org/10.1080/00927872.2016.1175615

Abstract

A formation F of finite groups has the generalized Wielandt property for residuals, or is a GWP-formation, if the F-residual of a group generated by two F-subnormal subgroups is the subgroup generated by their F-residuals. The main aim of the paper is to determine some suﬃcient conditions for a finite group to split over its F-residual.

2010 Mathematics subject classification: 20D10; 20D20

Keywords: Finite group; formation; residual; subnormality

# Paper “Finite groups with all minimal subgroups solitary” published in J. Algebra Appl.

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R. Esteban-Romero and Orieta Liriano.

Finite groups with all minimal subgroups solitary.

J. Algebra Appl., 15(8):1650140, 9, 2016

https://doi.org/10.1142/S0219498816501401

Abstract

We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order.

2010 Mathematical Subject Classification: 20D10, 20D30

Keywords: Finite group; solitary subgroup; minimal subgroup

# Paper “A Note on Solitary Subgroups of Finite Groups” published in Comm. Algebra

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R. Esteban-Romero and Orieta Liriano

A note on solitary subgroups of finite groups.

Comm. Algebra, 44(7):2945–2952, 2016

https://doi.org/10.1080/00927872.2015.1065855

Abstract

We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N. We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups.

2010 Mathematics Subject Classification: 20D10, 20D30, 20F16

Keywords: Finite group, Fitting class, Formation, Quotient solitary subgroup, Solitary subgroup

# Paper “On finite p-nilpotent groups” published in Monatsh. Math.

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Adolfo Ballester-Bolinches, Xiuyun Guo, Yangming Li, and Ning Su.

On finite p-nilpotent groups.

Monatsh. Math., 181(1):63–70, 2016

https://doi.org/10.1007/s00605-015-0803-y

Abstract

In this paper the structure of a minimal counterexample among the non-p-nilpotent groups having p-nilpotent p-Sylow normalisers is analysed. Several p-nilpotency criteria and many earlier results follow from our main theorem.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite groups, p-nilpotency, Minimal subgroups, Sylow normalisers

# Paper “Primitive subgroups and PST-groups” published in Bull. Aust. Math. Soc

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A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero

Primitive groups and PST-groups

Bull. Aust. Math. Soc., 89 (2014), 373–378

http://dx.doi.org/10.1017/S0004972713000592

Abstract

All groups considered in this paper are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as a proper subgroup. He et al. [‘A note on primitive subgroups of finite groups’, Commun. Korean Math. Soc. 28(1) (2013), 55–62] proved that every primitive subgroup of G has index a power of a prime if and only if G/Φ(G) is a solvable PST-group. Let X denote the class of groups G all of whose primitive subgroups have prime power index. It is established here that a group G is a solvable PST-group if and only if every subgroup of G is an X-group.

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

Keywords and phrases: finite groups, primitive subgroups, solvable PST-groups, T0-groups

# Charla de Guo Xiuyun

 Feb ’14 10 11:00

El profesor Guo Xiuyun, de la Universidad de Shanghai, impartirá la charla titulada

«The automizers and normalizers in finite groups»

el próximo lunes 10 de febrero de 2014, a las 11.00, en el seminario del Departament d’Àlgebra de la Universitat de València (2º piso de la Facultat de Matemàtiques).

# Paper “Primitive subgroups and PST-groups” to appear in Bull. Aust. Math. Soc.

The following paper has been accepted for publication. We will inform about the publication details.

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A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero

Primitive groups and PST-groups

Bull. Aust. Math. Soc.

http://dx.doi.org/10.1017/S0004972713000592

Abstract

All groups considered in this paper are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as a proper subgroup. He et al. [‘A note on primitive subgroups of finite groups’, Commun. Korean Math. Soc. 28(1) (2013), 55–62] proved that every primitive subgroup of G has index a power of a prime if and only if G/Φ(G) is a solvable PST-group. Let X denote the class of groups G all of whose primitive subgroups have prime power index. It is established here that a group G is a solvable PST-group if and only if every subgroup of G is an X-group.

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

Keywords and phrases: finite groups, primitive subgroups, solvable PST-groups, T0-groups

# Paper “On conjugacy of supplements of normal subgroups of finite groups” to appear in Bull. Aust. Math. Soc.

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A. Ballester-Bolinches, Luis M. Ezquerro,

On conjugacy of supplements of normal subgroups of finite groups

Bull. Aust. Math. Soc.

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 20D20.
Keywords and phrases: finite groups, supplements, Schunck classes, formations.