Equation 677 Database

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Magma 83783dd81aa2…

magma 83783dd81aa2
Size
705
Isomorphism class hash
83783dd81aa20fc654a707ad3eac7447cbf0f7551572ffdcc79c822f1f3cfa08
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 19:15:53
Display reorder
660,585,21,65,134,284,22,132,586,66,282,133,20,584,67,283,588,24,64,137,287,62,25,589,135,285,587,23,63,136,286,79,591,71,140,279,82,592,72,138,280,75,590,73,139,281,594,91,70,143,278,595,95,68,141,276,593,87,69,142,277,666,672,669,667,361,14,307,597,232,15,598,362,308,233,596,16,360,306,231,364,17,310,600,228,311,18,365,601,229,363,19,309,599,230,86,367,305,603,238,90,368,303,604,239,94,366,304,602,237,370,83,301,606,234,371,74,302,607,235,369,78,300,605,236,691,685,686,692,165,561,335,421,621,562,422,166,333,622,420,560,167,334,620,164,564,331,424,624,332,565,162,425,625,163,563,330,423,623,567,156,326,427,627,568,157,324,428,628,566,158,325,426,626,159,570,329,430,630,160,571,327,431,631,161,569,328,429,629,664,671,670,668,299,525,9,397,433,526,398,297,10,434,396,524,298,8,432,295,528,12,400,436,13,529,296,401,437,294,527,11,399,435,531,290,7,403,439,532,288,5,404,440,530,289,6,402,438,293,534,3,406,442,291,535,4,407,443,292,533,2,405,441,675,676,673,679,409,445,98,213,196,446,214,410,99,197,215,444,408,100,195,412,448,101,212,192,102,449,413,210,193,411,447,103,211,194,451,415,104,204,202,452,416,105,205,203,450,414,106,206,201,418,454,107,207,198,419,455,108,208,199,417,453,109,209,200,663,661,662,665,549,609,151,573,465,610,574,550,152,466,572,608,548,150,464,552,612,154,576,468,155,613,553,577,469,551,611,153,575,467,615,555,149,579,471,616,556,147,580,472,614,554,148,578,470,558,618,145,582,474,559,619,146,583,475,557,617,144,581,473,699,695,698,700,457,128,26,122,111,126,123,458,27,112,121,127,456,28,110,460,131,29,118,114,30,129,461,119,115,459,130,31,120,113,124,463,32,0,117,647,646,33,645,644,125,462,34,1,116,655,654,35,653,652,659,658,36,657,656,651,650,37,649,648,703,704,701,702,537,489,85,395,376,490,393,538,77,377,394,488,536,81,375,540,492,97,391,372,89,493,541,392,373,539,491,92,390,374,495,543,96,386,382,496,544,88,384,383,494,542,93,385,381,546,498,80,389,378,547,499,84,387,379,545,497,76,388,380,694,693,697,696,264,261,216,349,501,262,350,265,217,502,348,263,266,218,500,267,260,219,352,504,220,258,268,353,505,269,259,221,351,503,252,270,222,355,507,253,271,223,356,508,254,272,224,354,506,273,255,225,358,510,274,256,226,359,511,275,257,227,357,509,674,678,680,684,477,184,57,174,633,185,175,478,58,634,176,183,476,56,632,480,180,60,177,636,61,181,481,178,637,479,182,59,179,635,190,483,55,172,639,191,484,53,173,640,189,482,54,171,638,486,186,51,168,642,487,187,52,169,643,485,188,50,170,641,681,683,677,682,44,249,344,319,513,250,320,45,342,514,318,251,46,343,512,47,248,347,322,516,345,246,48,323,517,49,247,346,321,515,240,42,339,317,519,241,43,340,315,520,242,41,341,316,518,38,243,338,313,522,39,244,336,314,523,40,245,337,312,521,689,688,687,690 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#966159413732cc97ab9cbe48ea19b17c045c0e7dae7d4f88fdd62e86aa428734, 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 19:15:54 · history