Sylow Permutable Subnormal Subgroups of Finite Groups

Ballester‐Bolinches, A.; Esteban‐Romero, R.

doi:10.1006/jabr.2001.9138

Cited by 58 publications

(61 citation statements)

References 13 publications

(18 reference statements)

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“…(1) ⇒ (2). The proof is similar to the proof of (2) Now G/F a solvable PT -group and thus an X p -group for all primes p by Theorem 1, part (2). Hence the Sylow subgroups of G/F are Iwasawa.…”

Section: Resultsmentioning

confidence: 65%

Some local properties defining $\mathcal T_0$-groups and related classes of groups

Ballester‐Bolinches¹,

Beidleman²,

Esteban‐Romero³

et al. 2016

Publicacions Matemàtiques

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Abstract. We call G a Hall X -group if there exists a normal nilpotent subgroup N of Gis, one in which normality is a transitive relation. We present several new local classes of groups which locally define Hall X -groups and T 0 -groups where X ∈ {T , PT , PST }; the classes PT and PST denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.

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Section: Resultsmentioning

confidence: 65%

Some local properties defining $\mathcal T_0$-groups and related classes of groups

Ballester‐Bolinches¹,

Beidleman²,

Esteban‐Romero³

et al. 2016

Publicacions Matemàtiques

Self Cite

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“…These classes have been studied in detail, with many characterizations available (see [1], [2], [3], [4], [5], [6], [7], [14], [15]). …”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…Recall that, for a prime p, a group G satisfies property Y p if for each pair of psubgroups H and K of G with H c K, then H is S-permutable in N G ðKÞ (see [4]), and that G satisfies C p if every subgroup of a Sylow p-subgroup P of G is normal in N G ðPÞ (see [14]). …”

Section: Theoremmentioning

confidence: 99%

On self-normalizing subgroups of finite groups

Ballester‐Bolinches

Esteban‐Romero

Li³

2010

Journal of Group Theory

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“…Then G is not a PST -group, yet every proper subgroup has Y p and Y q , and thus is a PST -group by [2].…”

Section: Proofs Of Theorems 2 3 Andmentioning

confidence: 99%

“…Recall that a subgroup H is said to be Sylow-permutable, or S-permutable, in a group G if H permutes with every Sylow subgroup of G. We mention a similar class Y p , which was introduced in [2]. If p is a prime, a group G belongs to the class Y p if G enjoys the following property: if H and K are p-…”

Section: Introductionmentioning

confidence: 99%