Equation 677 Database

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Magma 4e095cedf71f…

magma 4e095cedf71f
Size
705
Isomorphism class hash
4e095cedf71f39cbc83c82e6b98187d181af0ac0cedfa58379bf1220421ff409
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 19:45:01
Display reorder
660,472,187,73,421,336,473,188,422,74,337,474,186,423,72,338,190,475,420,76,339,191,476,418,77,340,189,477,419,75,341,193,427,71,470,334,194,428,69,471,335,192,429,70,469,333,426,196,67,466,330,424,197,68,467,331,195,425,66,468,332,672,665,662,667,400,639,315,532,412,401,640,533,316,413,402,641,534,317,414,642,403,535,314,415,643,404,536,312,416,644,405,537,313,417,637,530,306,398,410,638,531,307,399,411,636,529,308,397,409,526,633,309,394,406,527,634,310,395,407,635,528,311,396,408,689,686,687,692,259,496,213,287,294,260,497,285,214,295,258,498,286,215,296,499,262,283,212,297,500,263,284,210,298,501,261,282,211,299,494,293,219,265,300,495,291,220,266,301,493,292,221,264,302,289,490,218,268,303,290,491,216,269,304,492,288,217,267,305,661,670,668,666,12,520,24,388,555,13,521,389,25,556,14,522,390,26,557,523,15,391,27,558,524,16,392,28,559,525,17,393,29,560,518,386,30,18,553,519,387,31,19,554,517,385,32,20,552,382,514,33,21,549,383,515,34,22,550,516,384,35,23,551,674,673,681,679,376,567,45,591,364,377,568,592,46,365,378,569,593,47,366,570,379,594,44,367,571,380,595,42,368,572,381,596,43,369,565,589,36,374,362,566,590,37,375,363,564,588,38,373,361,585,561,39,370,358,586,562,40,371,359,563,587,41,372,360,671,664,663,669,206,436,275,448,180,204,437,449,273,181,205,438,450,274,182,439,209,451,271,183,440,207,452,272,184,441,208,453,270,185,434,446,281,201,178,435,447,279,202,179,433,445,280,203,177,442,430,277,200,174,443,431,278,198,175,432,444,276,199,176,695,698,699,694,544,357,164,348,651,545,355,349,162,652,546,356,350,163,653,353,547,351,167,654,354,548,352,165,655,657,658,656,166,659,61,346,170,542,649,62,347,168,543,650,60,345,169,541,648,342,64,173,538,645,343,65,171,539,646,63,344,172,540,647,702,701,703,704,484,615,5,93,113,485,616,94,3,111,486,617,95,4,112,618,487,92,0,109,619,488,90,2,110,620,489,91,1,108,613,99,11,482,104,614,100,9,483,102,612,101,10,481,103,98,609,7,478,107,96,610,8,479,105,611,97,6,480,106,693,696,697,700,508,319,80,603,460,509,320,604,78,461,510,318,605,79,462,322,511,606,83,463,323,512,607,81,464,321,513,608,82,465,325,601,86,506,458,326,602,84,507,459,324,600,85,505,457,597,328,89,502,454,598,329,87,503,455,327,599,88,504,456,682,676,675,677,117,135,57,147,627,118,136,148,58,628,119,137,149,59,629,134,116,146,56,630,132,114,144,54,631,133,115,145,55,632,126,138,48,123,625,127,139,49,124,626,128,140,50,125,624,141,129,51,122,621,142,130,52,120,622,131,143,53,121,623,684,678,683,680,234,248,154,579,222,235,246,580,155,223,236,247,581,153,224,251,237,582,150,225,249,238,583,151,226,250,239,584,152,227,254,577,160,240,228,252,578,161,241,229,253,576,159,242,230,573,257,156,243,231,574,255,157,244,232,256,575,158,245,233,690,688,691,685 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#a6f8f14c2d1a7a50e2f04288a5c27cfc248015f3a737479d1ca25990a259c6e6, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 19:45:02 · history