Groups of Order 8 and 12: Semidirect Products of Groups

Loops which are semidirect products of groups

Acta Mathematica Hungarica ◽

10.1007/s10474-006-0529-3 ◽

2006 ◽

Vol 114 (3) ◽

pp. 247-266 ◽

Cited By ~ 3

Author(s):

Á. Figula ◽

K. Strambach

Keyword(s):

Semidirect Products ◽

Products Of Groups

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Using semidirect products of groups to build classes of interconnection networks

Discrete Applied Mathematics ◽

10.1016/j.dam.2019.12.014 ◽

2020 ◽

Vol 283 ◽

pp. 78-97

Author(s):

Iain A. Stewart

Keyword(s):

Interconnection Networks ◽

Semidirect Products ◽

Products Of Groups

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Loops which are semidirect products of groups

Communications in Algebra ◽

10.1080/00927879508825207 ◽

1995 ◽

Vol 23 (1) ◽

pp. 81-95 ◽

Cited By ~ 4

Author(s):

Gary F. Birkermeier ◽

Sihai Xiao

Keyword(s):

Semidirect Products ◽

Products Of Groups

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Congruences on the partial automorphism monoid of a free group action

International Journal of Algebra and Computation ◽

10.1142/s0218196721400075 ◽

2021 ◽

pp. 1-30

Author(s):

Matthew D. G. K. Brookes

Keyword(s):

Free Group ◽

Group Action ◽

Finite Rank ◽

Brandt Semigroup ◽

Semidirect Products ◽

Products Of Groups ◽

Free Group Action

We study congruences on the partial automorphism monoid of a finite rank free group action. We determine a decomposition of a congruence on this monoid into a Rees congruence, a congruence on a Brandt semigroup and an idempotent separating congruence. The constituent parts are further described in terms of subgroups of direct and semidirect products of groups. We utilize this description to demonstrate how the number of congruences on the partial automorphism monoid depends on the group and the rank of the action.

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