Equation 677 Database

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Magma 24201d7d35fe…

magma 24201d7d35fe
Size
707
Isomorphism class hash
24201d7d35fe81283765ef5f1cb0bfb758be563c23071c78b9103438d9bb36ff
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
2026-10-06 16:53:31
Display reorder
131,136,132,133,134,135,706,71,70,67,68,69,66,73,72,74,75,76,77,247,246,248,249,250,251,12,17,13,14,15,16,254,253,255,256,257,252,301,300,302,303,304,305,80,79,81,82,83,78,334,333,335,331,330,332,87,86,88,89,84,85,8,7,9,10,11,6,130,129,125,126,127,128,469,468,467,472,470,471,476,478,477,474,475,473,395,394,393,390,391,392,412,411,413,410,408,409,354,355,359,357,358,356,401,400,399,398,396,397,594,595,596,597,598,599,603,605,604,601,602,600,406,405,407,402,403,404,648,646,638,632,639,649,650,647,640,678,685,689,687,684,705,704,702,690,701,703,307,306,309,310,311,308,201,200,202,203,198,199,169,168,170,171,172,167,328,327,329,326,324,325,195,194,196,197,192,193,35,34,30,31,32,33,162,161,163,164,165,166,151,150,152,153,154,149,158,157,159,160,155,156,40,39,41,36,37,38,65,64,60,61,62,63,493,492,491,496,494,495,451,450,449,452,453,454,455,457,456,459,460,458,443,442,441,438,439,440,444,445,587,447,448,446,578,580,579,575,576,577,516,515,517,518,519,520,479,481,480,483,484,482,343,342,344,345,346,347,618,635,613,637,614,636,641,631,644,657,691,700,668,661,698,681,688,663,672,686,49,48,51,52,53,50,113,112,108,109,110,111,18,23,19,20,21,22,273,272,274,275,270,271,263,262,258,259,260,261,102,107,103,104,105,106,221,220,216,217,218,219,282,287,283,284,285,286,281,280,276,277,278,279,4,3,5,1,0,2,24,29,25,26,27,28,539,541,540,542,543,544,550,549,548,545,546,547,592,591,593,590,589,588,362,361,360,363,364,365,370,369,371,368,366,367,572,574,573,569,570,571,552,551,553,554,555,556,563,565,564,567,568,566,534,533,535,536,537,538,607,634,606,616,633,615,612,630,617,660,692,696,676,665,697,699,673,670,666,682,222,227,224,225,226,223,294,299,295,296,297,298,54,59,55,56,57,58,290,289,291,292,293,288,240,245,241,242,243,244,213,212,214,215,210,211,92,91,93,94,95,90,230,229,231,232,233,228,96,101,97,98,99,100,42,47,43,44,45,46,238,237,239,234,235,236,414,416,415,417,418,419,423,425,424,421,422,420,428,427,426,429,430,431,352,351,353,350,348,349,584,586,585,582,583,581,376,375,377,373,374,372,382,381,383,378,379,380,532,531,530,527,528,529,561,560,562,557,558,559,608,610,619,609,611,620,643,645,642,680,683,679,693,667,695,694,674,675,671,677,144,143,146,147,148,145,140,139,141,142,137,138,312,313,314,315,316,317,187,186,188,189,190,191,204,209,205,206,207,208,185,183,179,180,181,182,122,121,123,124,184,120,115,114,116,117,118,119,176,175,177,178,173,174,323,322,319,318,320,321,269,268,264,265,266,267,434,433,432,437,435,436,486,485,487,490,488,489,337,338,336,340,341,339,500,502,501,498,499,497,389,388,387,384,385,386,507,506,508,504,505,503,509,511,510,514,512,513,525,524,526,523,521,522,463,462,461,465,466,464,625,623,624,621,627,622,628,629,626,654,664,669,658,651,662,659,656,652,653,655 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#83fb73755ed07f789756511d0e776415c2bd28bb0aaa387c6c265081499d5ced, M = {6, 7, 8, 9, 10, 11, 135} 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 2026-10-06 16:53:32 · history