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 u...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...