Equation 677 Database

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Magma 22d027694fa5…

magma 22d027694fa5
Size
707
Isomorphism class hash
22d027694fa5dd9443c5e5f0d24b857dd487750f784400fc1e8a535932b45df1
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 03:17:05
Display reorder
301,302,300,305,303,304,656,50,49,48,53,51,52,163,162,164,167,165,166,102,104,103,107,105,106,222,224,223,227,225,226,219,221,220,218,216,217,159,161,160,158,157,156,135,137,136,133,134,132,146,144,145,147,148,149,92,91,90,95,93,94,172,171,173,168,169,170,465,464,466,467,462,463,530,529,531,532,533,528,593,592,588,589,590,591,479,478,474,475,476,477,603,602,604,605,601,600,505,504,506,507,508,509,451,450,452,453,454,455,524,523,525,526,527,522,511,510,512,513,514,515,554,553,555,556,557,552,616,612,606,626,607,627,635,641,617,633,677,674,673,689,706,676,693,686,675,691,80,79,78,83,81,82,120,122,121,124,125,123,269,268,267,264,266,265,155,154,153,150,152,151,88,87,89,84,85,86,192,194,193,197,195,196,243,245,244,240,242,241,273,275,274,270,272,271,74,73,72,77,75,76,295,294,296,297,298,299,578,577,579,580,581,576,383,382,378,379,380,381,480,485,481,482,483,484,412,411,413,408,409,410,536,535,537,538,539,534,355,354,356,357,358,359,402,407,403,404,405,406,448,447,449,444,445,446,349,348,350,351,352,353,549,548,550,551,546,547,655,646,630,649,643,647,632,634,618,638,695,703,697,670,705,678,704,698,699,692,34,33,35,31,32,30,129,131,130,127,128,126,99,101,100,98,96,97,15,17,16,14,12,13,211,212,210,213,214,215,59,58,57,55,56,54,185,184,183,180,181,182,119,118,117,114,115,116,280,279,281,276,278,277,290,289,288,292,293,291,366,371,367,368,369,370,399,398,400,401,396,397,585,584,586,587,582,583,599,598,594,595,596,597,420,425,421,422,423,424,490,489,491,486,487,488,544,543,545,540,541,542,516,521,517,518,519,520,324,329,325,326,327,328,562,561,563,558,559,560,648,644,642,650,631,651,628,636,629,620,696,701,700,659,690,657,681,688,680,658,67,66,68,70,71,69,142,141,143,140,139,138,252,253,254,255,256,257,5,4,3,0,2,1,187,186,188,189,190,191,10,9,11,6,7,8,234,235,236,239,237,238,246,247,248,251,249,250,258,259,260,262,263,261,282,283,284,285,286,287,388,387,389,384,385,386,460,459,461,456,457,458,435,434,436,437,432,433,330,335,331,332,333,334,496,495,497,492,493,494,429,428,430,431,426,427,374,373,375,376,377,372,575,574,570,571,572,573,565,564,566,567,568,569,343,342,344,345,346,347,653,645,639,654,637,652,615,640,625,624,702,687,685,671,683,679,694,684,682,672,41,40,39,38,36,37,27,29,28,25,26,24,206,205,204,208,209,207,202,201,203,198,199,200,233,232,231,228,230,229,19,18,20,21,22,23,61,60,62,65,63,64,178,177,179,176,174,175,42,44,43,45,46,47,112,111,113,108,109,110,307,311,306,308,309,310,312,317,313,314,315,316,318,323,319,320,321,322,362,361,363,364,365,360,442,441,443,438,439,440,500,499,501,502,503,498,340,339,341,336,337,338,469,468,470,471,472,473,419,418,414,415,416,417,392,391,393,394,395,390,619,611,609,623,608,622,614,621,610,613,662,661,660,669,663,668,665,666,667,664 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#f44078deebe7730562c927e2829a32c42b90cd1087b6200dbe445a4d4d2f9fa6, M = {42, 43, 44, 45, 46, 47, 128} 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 03:17:06 · history