Equation 677 Database

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Magma 51ea9194208a…

magma 51ea9194208a
Size
707
Isomorphism class hash
51ea9194208a6aa1cc9db4a9398f8bb0960aa88ea2e7e1df11b0513b5753e707
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
2026-10-08 22:12:30
Display reorder
362,361,363,364,365,360,671,49,48,50,52,53,51,329,328,327,324,325,326,181,180,182,185,183,184,140,139,138,141,142,143,135,137,136,134,132,133,179,178,177,175,176,174,145,144,146,148,149,147,42,44,43,47,45,46,188,187,186,189,190,191,159,161,160,156,157,158,154,153,155,152,150,151,424,423,425,426,427,422,397,396,392,393,394,395,354,359,355,356,357,358,372,377,373,374,375,376,400,399,401,402,403,398,390,389,391,386,387,388,420,419,421,416,417,418,563,562,564,565,596,591,593,597,592,595,594,566,613,636,631,659,635,634,629,628,630,627,625,690,697,706,665,705,675,661,687,688,28,27,29,24,26,25,17,16,15,12,13,14,54,56,55,58,59,57,318,320,319,322,323,321,1,2,0,5,3,4,23,22,21,19,20,18,60,62,61,63,64,65,227,226,225,223,224,222,302,301,300,303,304,305,297,299,298,294,295,296,293,292,291,288,289,290,600,599,601,598,528,529,441,440,442,443,444,445,533,532,534,535,531,530,432,431,433,428,429,430,347,346,342,343,344,345,451,450,446,447,448,449,545,544,546,578,579,577,590,589,587,588,558,559,513,512,514,515,516,571,607,654,653,608,614,609,615,658,652,610,641,666,694,667,691,693,678,681,683,680,104,103,102,107,105,106,215,214,213,210,211,212,67,66,68,71,69,70,233,232,231,228,229,230,216,218,217,221,219,220,98,97,96,100,101,99,209,208,207,206,204,205,248,247,246,250,251,249,38,37,36,39,40,41,163,162,164,166,167,165,260,259,258,261,262,263,465,464,466,467,468,469,553,552,554,555,551,550,348,353,349,350,351,352,508,507,509,510,511,506,335,334,331,330,332,333,336,341,337,338,339,340,537,536,538,575,573,574,584,583,585,586,556,557,518,517,519,520,521,572,621,612,632,639,616,642,656,660,646,640,649,699,698,668,695,696,686,685,679,664,284,282,283,287,285,286,264,266,265,268,269,267,93,95,94,91,92,90,193,192,194,197,195,196,77,76,75,73,74,72,78,80,79,83,81,82,128,127,126,131,129,130,7,6,8,9,10,11,109,108,110,113,111,112,310,309,311,307,308,306,315,317,316,313,314,312,602,605,603,604,560,561,407,406,408,409,404,405,486,485,487,482,483,484,471,470,472,473,474,475,490,489,491,492,493,488,495,494,496,497,498,499,548,547,549,580,581,582,570,569,567,568,384,385,540,539,541,542,543,576,651,622,655,647,620,618,626,637,657,617,606,689,692,682,662,677,676,663,684,700,238,237,239,235,236,234,169,168,170,173,171,172,121,120,122,125,123,124,115,114,116,119,117,118,279,281,280,278,276,277,31,30,32,33,34,35,274,273,275,271,272,270,199,198,200,201,202,203,252,254,253,256,257,255,241,240,242,244,245,243,88,87,89,86,84,85,461,460,462,463,458,459,383,382,378,379,380,381,369,368,370,371,366,367,410,415,411,412,413,414,481,480,476,477,478,479,456,455,457,452,453,454,501,500,502,503,504,505,437,436,438,439,434,435,524,522,525,526,527,523,643,645,644,633,624,611,648,623,619,650,638,670,669,701,703,674,672,673,704,702 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#54e3a19f93137e404c924a9b37966faa8299b270c95916aef4ed0fa8730aa82d, M = {108, 109, 110, 111, 112, 113, 139} 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 2026-10-08 22:12:31 · history