Equation 677 Database

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Magma 4ea1196b188b…

magma 4ea1196b188b
Size
707
Isomorphism class hash
4ea1196b188bcb5c877fa4a263596692f794309fbde17a1477ab1e9f1d1b2e32
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 09:59:54
Display reorder
305,304,303,301,300,302,656,119,117,116,114,115,118,107,106,105,102,103,104,218,217,216,221,219,220,180,182,181,183,184,185,295,296,294,298,299,297,76,75,77,74,72,73,96,98,97,100,101,99,69,71,70,66,67,68,108,110,109,112,113,111,257,256,255,253,252,254,469,468,470,471,472,473,599,598,594,595,596,597,485,484,480,481,482,483,491,490,486,487,488,489,475,474,476,477,478,479,568,567,569,565,564,566,347,346,342,343,344,345,405,404,406,407,402,403,602,601,603,604,605,600,496,495,497,492,493,494,633,630,611,606,615,614,627,618,634,648,699,706,704,702,679,690,680,689,693,692,202,203,199,200,198,201,215,214,213,210,211,212,209,208,207,206,204,205,260,258,259,263,261,262,289,290,288,292,293,291,148,147,149,146,144,145,137,136,135,132,133,134,246,247,248,250,251,249,65,64,63,60,61,62,143,142,141,138,139,140,357,356,358,359,354,355,378,383,379,380,381,382,500,499,501,502,503,498,461,460,456,457,458,459,511,510,512,513,514,515,577,581,576,578,579,580,349,348,350,351,352,353,543,542,544,545,540,541,397,396,398,399,400,401,444,449,445,446,447,448,654,650,640,624,641,643,631,622,636,649,691,698,696,697,678,695,663,694,688,687,81,82,78,79,80,83,5,4,3,1,0,2,43,42,44,46,47,45,160,159,161,157,158,156,222,223,224,227,225,226,150,152,151,154,155,153,56,55,54,57,58,59,196,195,197,193,194,192,229,230,228,232,233,231,127,126,128,131,129,130,466,465,467,462,463,464,455,454,450,451,452,453,408,413,409,410,411,412,527,526,522,523,524,525,591,590,592,593,588,589,521,520,516,517,518,519,537,536,538,539,534,535,585,584,586,587,583,582,559,558,560,561,562,563,572,571,573,574,570,575,651,652,637,621,639,645,619,620,628,644,686,700,701,673,677,669,672,683,681,668,265,264,267,268,269,266,37,38,36,40,41,39,282,283,284,286,287,285,278,276,277,281,279,280,190,189,191,188,186,187,10,9,11,8,6,7,88,87,89,86,84,85,21,23,22,18,19,20,234,235,236,239,237,238,273,275,274,270,272,271,327,326,328,329,324,325,370,369,371,366,367,368,425,424,420,421,422,423,386,385,387,388,389,384,426,431,427,428,429,430,335,334,330,331,332,333,414,419,415,416,417,418,554,553,555,556,557,552,546,551,547,548,549,550,338,337,339,340,341,336,655,653,638,625,646,647,616,617,635,642,703,685,705,674,671,675,670,682,676,684,243,244,240,241,242,245,24,26,25,28,29,27,33,35,34,30,31,32,94,93,95,91,92,90,162,164,163,166,167,165,170,169,168,171,172,173,175,174,176,179,177,178,120,122,121,123,124,125,14,13,12,15,16,17,51,53,52,49,50,48,506,505,507,508,509,504,319,318,320,321,322,323,433,432,434,435,436,437,309,308,310,311,307,306,393,392,394,395,390,391,438,443,439,440,441,442,313,312,314,315,316,317,530,529,531,532,533,528,364,363,365,360,361,362,377,376,372,373,374,375,629,626,613,607,610,609,612,608,623,632,662,666,664,658,660,667,665,661,659,657 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#fd7de578af0812c41995e8ffd4ad83dcb5427b7eb760f7a58401ca67989e247a, M = {18, 19, 20, 21, 22, 23, 136} 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 09:59:55 · history