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Periodic linear groups factorized by mutually permutable subgroups

Maria Ferrara, Marco Trombetti (2023)

Czechoslovak Mathematical Journal

The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic...

Periodic subgroups of projective linear groups in positive characteristic

Alla Detinko, Dane Flannery (2008)

Open Mathematics

We classify the maximal irreducible periodic subgroups of PGL(q, 𝔽 ), where 𝔽 is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and 𝔽 × has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, 𝔽 ) containing the centre 𝔽 ×1q of GL(q, 𝔽 ), such that G/ 𝔽 ×1q is a maximal periodic subgroup of PGL(q, 𝔽 ), and if H is another group of this kind then H is GL(q, 𝔽 )-conjugate to a group in the list. We give criteria for determining...

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