Permutation groups with cyclic-block property and MNFCMNFCMNFC-groups

Ali Osman ASAR

Article Details

Permutation groups with cyclic-block property and MNFCMNFCMNFC-groups

Authors:

Ali Osman ASAR

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2017 Vol.41 Issue 4, pp.983-997

Document Type:

Article

Publication Date:

7/2017

Document Language:

Turkish

Document ID (Org No.):

2000746027

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

This work continues the investigation of perfect  locally finite minimal non-FCFCFC-groups in totally imprimitive  permutation ppp-groups. At present, the class of totally  imprimitive permutation ppp-groups satisfying the cyclic-block  property is known to be the only class of ppp-groups having common  properties with a hypothetical minimal non-FCFCFC-group, because a  totally imprimitive permutation ppp-group satisfying the  cyclic-block property cannot be generated by a subset of finite  exponent and every non-FCFCFC-subgroup of it is transitive, which  are the properties satisfied by a minimal non-FCFCFC-group. Here a  sufficient condition is given for the nonexistence of minimal  non-FCFCFC-groups in this class of permutation groups. In particular,  it is shown that the totally imprimitive permutation ppp-group  satisfying the cyclic-block property that was constructed earlier  and its commutator subgroup cannot be minimal non-FCFCFC-groups.  Furthermore, some properties of a maximal ppp-subgroup of the  finitary symmetric group on N∗N∗\mathbb{N}^* are obtained.

Article Details

Permutation groups with cyclic-block property and MNFCMNFCMNFC-groups

Authors: Ali Osman ASAR

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2017 Vol.41 Issue 4, pp.983-997

Document Type: Article

Publication Date: 7/2017

Document Language: Turkish

Document ID (Org No.): 2000746027

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Ali Osman ASAR

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2017 Vol.41 Issue 4, pp.983-997

Document Type:

Article

Publication Date:

7/2017

Document Language:

Turkish

Document ID (Org No.):

2000746027

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098