Abstract The aim of the paper is to provide a large extension recent results de Giovanni and Ialenti (Commun Algebra 44:118–124, 2016), strengthening at same time their conclusions. Our second main theorem actually complete generalization result obtained in finite case by Beidleman Heineken (Arch Math (Basel) 85:18–30, 2005) periodic linear groups.

We present a refutation system for intuitionistic logic which allows to locate situations where constructive reasoning is unnecessary. In many subgoals of a derivation this property makes it possible to reduce the set of relevant reduction rules to a connuent one. As a result, back-tracking over choicepoints for diierent orderings of non-permutable rules can often be avoided and the search spac...

The second author introduced notions of weak permutablity and commutativity between groups and proved the finiteness of a group generated by two weakly permutable finite subgroups. Two groups H, K weakly commute provided there exists a bijection f : H → K which fixes the identity and such that h commutes with its image h for all h ∈ H. The present paper gives support to conjectures about the ni...