GROUPS AND ULTRA-GROUPS

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Moghaddasi Gh.; ZOLFAGHARI P.; TOLUE HAGHIGHI B.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2017 | Volume:3 | Issue:10 Page(s): 107-116

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Information Journal Paper

Title

GROUPS AND ULTRA-GROUPS

Author(s)

Moghaddasi Gh. | ZOLFAGHARI P. | TOLUE HAGHIGHI B. | Issue Writer Certificate

Keywords

COSETQ1

TRANSVERSALQ1

HOMOMORPHISMQ1

ULTRA-GROUPQ1

Abstract

In this paper, in addition to some elementary facts about the ULTRA-GROUPs, which their structure based on the properties of the TRANSVERSAL of a subgroup of a group, we focus on the relation between a group and an ULTRA-GROUP. It is verified that every group is an ULTRA-GROUP, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an ULTRA-GROUP over a group, there exists a normal subgroup of that certain group. Moreover, by proving this feature that a monomorphism in groups preserve the ULTRA-GROUPs over groups, we show that, corresponding to any monomorphism in groups, there is an ultragroup HOMOMORPHISM on the subgroups of those groups. Finally, we prove isomorphism theorems for ULTRA-GROUPs. These theorems connect three notions subultra-group, normal subultra-group, quotient ULTRA-GROUP, and directly, similar to the isomorphism theorems in group theory and module theory are proved.

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APA: Copy

Moghaddasi, Gh., ZOLFAGHARI, P., & TOLUE HAGHIGHI, B.. (2017). GROUPS AND ULTRA-GROUPS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(10), 107-116. SID. https://sid.ir/paper/257311/en

Vancouver: Copy

Moghaddasi Gh., ZOLFAGHARI P., TOLUE HAGHIGHI B.. GROUPS AND ULTRA-GROUPS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2017;3(10):107-116. Available from: https://sid.ir/paper/257311/en

IEEE: Copy

Gh. Moghaddasi, P. ZOLFAGHARI, and B. TOLUE HAGHIGHI, “GROUPS AND ULTRA-GROUPS,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 10, pp. 107–116, 2017, [Online]. Available: https://sid.ir/paper/257311/en

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