Relation between the left and right cosets of an α-normal subgroup
2021 ◽
Vol 2106
(1)
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pp. 012023
Abstract Let G be a group and α be an automorphism of G. In 2016, Ganjali and Erfanian introduced the notion of a normal subgroup related to α, called the α-normal subgroup. It is basically known that if N is an ordinary normal subgroup of G then every right coset Ng is actually the left coset gN. This fact allows us to define the product of two right cosets naturally, thus inducing the quotient group. This research investigates the relation between the left and right cosets of the relative normal subgroup. As we have done in the classic version, we then define the product of two right cosets in a natural way and continue with the construction of a, say, relative quotient group.
1989 ◽
Vol 41
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pp. 14-67
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2008 ◽
Vol 7
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pp. 751-792
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1987 ◽
Vol 102
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pp. 411-420
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1969 ◽
Vol 65
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pp. 409-430
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2000 ◽
Vol 61
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pp. 27-32
2021 ◽
Vol 35
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pp. 103-119
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1972 ◽
Vol 24
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pp. 1086-1091
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2016 ◽
Vol 95
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pp. 338-346
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