Intermediately fully invariant subgroups of abelian groups

Chekhlov, A. R.

doi:10.1134/s0037446617050184

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“…Because of every fully invariant subgroup is a normal [7,8]. Thus, the normal closure of S(A n ) is A n .…”

Section: Proofmentioning

confidence: 99%

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Square root of an element in $PSL_2(\mathbb{F}_p)$, $SL_2(\mathbb{F}_p)$, $GL_2(\mathbb{F}_p)$ and $A_n$. Verbal width by set of squares in alternating group $A_n$ and Mathieu groups

Ruslan¹

2021

Preprint

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In this paper questions of the width in verbal subgroups of A n is considered. Verbal width by set of squares of alternating group is found, it is happened equals to 2. The criterion of squareness in A n is presented. The necessary and sufficient conditions when an element of alternating group can be presented as a squares of one element are also found by us. Some necessary conditions to an element g ∈ A n being the square in A n are investigated.

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“…Because of every fully invariant subgroup is a normal [7,8]. Thus, the normal closure of S(A n ) is A n .…”

Section: Proofmentioning

confidence: 99%

“…In other words, we can claim. Since any verbal subgroup of any group is a fully invariant subgroup [7,11]…”

Section: Proofmentioning

confidence: 99%