9 citations · 12 across the 8 of their papers we have counts for
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On the common transversal probability in finite groups
S. Aivazidis, M. Loukaki, T. W. Mueller
Let be a finite group, and let be a subgroup of . We compute the probability, denoted by , that a left transversal of in is also a right transversal, thu…
Large subgroups in finite groups
Stefanos Aivazidis, Thomas W. Müller
Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if , so that N has bounded index in G. Our principal aim here is to est…
On residuals of finite groups
Stefanos Aivazidis, Thomas Mueller
A theorem of Dolfi, Herzog, Kaplan, and Lev \cite[Thm.~C]{DHKL} asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bound…
Group actions, deformations, polygroup extensions, and group presentations
Serban A. Basarab, Thomas W. Müller
Generalizing classical extension theory, we solve a Schreier-type extension problem for polygroups by groups. As a consequence, we obtain a method for computing a presentation for…
Normalising graphs of groups
Christian Krattenthaler, Thomas W. Müller
We discuss a partial normalisation of a finite graph of finite groups which leaves invariant the fundamental group. In conjunction with an easy graph-theoretic result,…
Free subgroup numbers modulo prime powers: the non-periodic case
Christian Krattenthaler, Thomas W. Müller
In [J. Algebra 452 (2016), 372-389], we characterise when the sequence of free subgroup numbers of a finitely generated virtually free group is ultimately periodic modulo a giv…