Equation 677 Database

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Magma 81c2b33a0572…

magma 81c2b33a0572
Size
707
Isomorphism class hash
81c2b33a0572c73703be05bb34907ad590618a3b6b7683fd2e444ec014710c54
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 13:09:36
Display reorder
601,600,602,603,604,605,706,588,561,586,578,596,113,567,146,121,143,137,106,535,550,574,545,532,119,554,589,575,562,587,579,597,108,568,147,122,138,132,107,534,551,555,541,528,114,590,570,563,582,580,598,109,569,148,123,139,133,102,536,547,556,540,529,115,591,571,559,583,581,599,110,564,149,124,140,134,103,537,546,557,542,530,116,592,572,558,584,576,594,111,565,144,125,141,135,104,538,548,553,543,531,117,593,573,560,585,577,595,112,566,145,120,142,136,105,539,549,552,544,533,118,127,129,130,131,126,128,628,631,626,629,630,627,700,705,701,702,704,699,703,654,657,653,658,655,656,659,323,14,31,78,328,316,176,188,520,382,509,395,496,461,90,238,87,51,370,318,91,15,32,79,329,317,177,189,521,383,504,390,497,456,371,239,88,52,319,92,16,33,80,324,312,178,190,516,378,505,391,492,457,366,234,89,53,320,93,17,34,81,325,313,179,191,517,379,506,392,493,458,367,235,84,48,321,94,12,35,82,326,314,174,186,518,380,507,393,494,459,368,236,85,49,322,95,13,30,83,327,315,175,187,519,381,508,394,495,460,369,237,86,50,68,70,71,66,67,69,676,677,675,674,672,673,650,652,648,633,649,647,651,684,683,681,682,679,680,678,416,358,192,472,490,262,454,274,431,54,25,407,443,18,171,184,361,240,266,417,172,359,193,473,491,263,455,275,426,55,26,402,438,19,267,185,362,241,418,173,354,194,469,486,258,450,270,427,56,27,403,439,20,268,180,363,242,419,168,355,195,468,487,259,451,271,428,57,28,404,440,21,269,181,364,243,415,169,356,196,470,488,260,452,272,429,58,29,405,441,22,264,182,365,244,414,170,357,197,471,489,261,453,273,430,59,24,406,442,23,265,183,360,245,162,164,165,166,167,163,669,666,665,668,660,664,645,637,640,635,641,643,639,694,696,689,697,687,691,686,287,400,424,478,466,448,436,527,389,503,377,221,515,331,307,279,230,96,412,282,308,401,425,479,467,449,437,522,384,498,372,216,510,332,413,280,231,97,283,309,396,420,474,462,444,432,523,385,499,373,217,511,333,408,281,232,98,284,310,397,421,475,463,445,433,524,386,500,374,218,512,334,409,276,233,99,285,311,398,422,476,464,446,434,525,387,501,375,219,513,335,410,277,228,100,286,306,399,423,477,465,447,435,526,388,502,376,220,514,330,411,278,229,101,304,300,301,302,303,305,662,663,661,670,667,671,642,646,636,638,634,644,632,698,685,690,692,695,688,693,255,47,4,209,65,247,154,292,161,7,202,72,340,347,350,227,210,40,299,256,351,42,5,204,60,248,155,293,156,8,203,73,341,342,294,222,211,41,257,352,43,1,205,61,249,150,288,157,9,198,74,336,343,295,223,212,36,252,353,44,0,206,62,250,151,289,158,10,199,75,337,344,296,224,213,37,253,348,45,2,207,63,251,152,290,159,11,200,76,338,345,297,225,214,38,254,349,46,3,208,64,246,153,291,160,6,201,77,339,346,298,226,215,39,483,485,480,481,482,484,615,620,616,619,621,622,618,625,607,624,614,617,623,609,608,606,610,611,612,613 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#ab7663272fb322647e3a6f8af752cc36283f2dfca26817d870d65fdaf95a91e5, M = {13, 34, 54, 74, 94, 114, 138} 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 13:09:37 · history