Equation 677 Database

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Magma e233f81706ce…

magma e233f81706ce
Size
707
Isomorphism class hash
e233f81706ce400452ffdccf88339f8f4868af12cc405350c53a7071b5ed2744
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-09 00:21:52
Display reorder
110,109,111,112,113,108,706,321,323,322,319,320,318,281,280,277,276,278,279,181,180,182,183,184,185,197,196,192,193,194,195,287,286,283,282,284,285,223,222,224,225,226,227,246,251,247,248,249,250,234,239,235,236,237,238,203,202,198,199,200,201,332,330,333,334,335,331,326,325,324,327,328,329,382,381,383,378,379,380,533,532,531,530,528,529,481,480,482,485,483,484,468,470,469,472,473,471,496,495,494,493,492,515,514,513,512,510,511,509,353,352,351,349,350,348,365,364,363,362,360,361,374,373,372,376,377,375,616,615,614,607,618,617,629,642,634,669,673,664,689,695,703,694,700,699,705,704,296,298,297,295,294,299,164,163,165,166,167,162,304,303,305,301,300,302,66,71,67,68,69,70,30,35,31,32,33,34,79,78,80,81,82,83,91,90,92,93,94,95,17,16,12,13,14,15,41,40,36,37,38,39,168,173,169,170,171,172,10,9,11,6,7,8,384,386,385,389,387,388,416,415,414,419,417,418,410,409,408,411,412,413,403,402,404,407,405,406,521,520,519,518,516,517,343,342,344,345,346,347,544,543,545,540,541,542,595,596,594,597,598,599,550,549,551,546,547,548,621,622,619,620,623,625,628,639,624,654,690,677,666,678,687,665,691,676,696,701,306,309,308,311,307,310,59,58,54,55,56,57,48,53,49,50,51,52,151,150,152,153,154,155,45,44,46,47,42,43,267,266,268,269,264,265,260,259,261,262,263,258,2,0,3,4,5,1,77,76,72,73,74,75,156,161,157,158,159,160,65,64,60,61,62,63,538,537,539,534,535,536,395,394,393,392,390,391,578,576,577,579,580,581,359,358,357,354,355,356,583,584,582,585,586,587,422,421,420,424,425,423,571,572,570,573,574,575,466,465,467,463,464,462,590,589,588,592,593,591,631,627,635,630,636,633,626,640,632,662,688,674,667,680,685,670,671,686,684,702,314,316,315,313,312,317,140,139,141,142,143,138,117,116,118,119,114,115,89,88,84,85,86,87,214,213,215,210,211,212,103,102,104,105,106,107,100,99,101,96,97,98,123,122,124,125,120,121,132,137,133,134,135,136,126,131,127,128,129,130,145,144,146,147,148,149,449,448,447,445,446,444,559,558,560,562,563,561,564,566,565,568,569,567,601,602,600,604,605,603,438,440,439,441,442,443,433,432,434,435,436,437,458,457,456,460,461,459,452,451,450,455,453,454,427,426,428,429,430,431,646,637,643,638,644,641,645,647,648,682,668,661,693,681,692,679,672,683,698,697,291,293,292,289,290,288,275,274,270,271,272,273,209,208,204,205,206,207,24,29,25,26,27,28,257,256,252,253,254,255,22,21,23,18,19,20,189,188,190,191,186,187,228,233,229,230,231,232,175,174,176,177,178,179,245,244,240,241,242,243,216,221,217,218,219,220,399,401,400,398,396,397,497,499,498,500,501,502,508,507,506,503,504,505,475,474,476,479,477,478,487,486,488,490,491,489,555,557,556,554,553,552,527,526,525,523,524,522,367,366,368,370,371,369,336,337,338,339,340,341,611,613,612,606,609,608,610,650,649,652,655,653,660,657,658,651,659,656,663,675 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#51f9b7d09d33f9fd9b24ec352fcf17309682f23da1a55124c3f963e5739f1055, M = {66, 67, 68, 69, 70, 71, 144} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 101.

last edited by qawbecrdtey at 2026-10-09 00:21:54 · history