Equation 677 Database

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Magma b7045799d73a…

magma b7045799d73a
Size
705
Isomorphism class hash
b7045799d73acb4e083a78c9d68e3ff305c5c2a032edae574731e243243d833e
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 19:46:17
Display reorder
660,3,577,578,566,567,598,4,586,587,597,558,557,5,546,547,637,638,2,626,627,657,658,1,646,647,617,618,0,606,607,526,537,9,538,527,497,10,498,486,487,517,11,518,506,507,8,448,449,443,444,6,475,476,465,466,7,435,436,425,426,696,692,698,694,69,579,563,572,562,583,70,592,582,599,543,559,71,552,542,639,623,68,632,622,659,643,66,652,642,619,603,67,612,602,532,539,60,523,522,499,61,483,492,482,519,62,503,512,502,63,457,450,446,441,64,477,462,471,460,65,437,422,431,420,699,702,691,687,89,36,163,32,415,164,87,30,416,37,162,38,88,31,414,39,166,85,35,418,40,167,86,33,419,41,165,84,34,417,27,42,95,161,413,43,93,159,28,411,44,94,160,29,412,91,45,157,26,409,92,46,158,24,410,90,47,156,25,408,668,667,682,664,231,136,217,391,355,218,232,392,356,137,216,135,233,390,354,132,220,230,394,358,133,221,228,395,359,134,219,229,393,357,389,142,237,223,353,143,238,224,387,351,141,239,222,388,352,236,138,226,385,349,234,139,227,386,350,235,140,225,384,348,670,665,674,678,54,561,575,573,571,595,55,593,591,581,555,541,56,553,551,620,635,57,633,631,640,655,58,653,651,601,615,59,613,611,533,520,52,535,531,481,53,495,493,491,501,51,515,513,511,48,440,447,455,454,49,461,474,472,470,50,421,434,432,430,690,704,693,697,184,564,568,574,570,588,185,594,590,584,548,544,183,554,550,624,628,180,634,630,644,648,181,654,650,604,608,182,614,610,534,524,190,528,530,484,191,488,494,490,504,189,508,514,510,186,451,452,456,453,187,463,467,473,469,188,423,427,433,429,688,686,703,689,210,560,576,565,569,596,211,585,589,580,556,540,212,545,549,621,636,213,625,629,641,656,214,645,649,600,616,215,605,609,525,521,208,536,529,480,209,496,485,489,500,207,516,505,509,204,459,458,442,445,205,479,478,464,468,206,439,438,424,428,685,700,695,701,96,343,379,331,76,380,97,332,77,344,378,342,98,330,75,346,382,99,334,72,347,383,100,335,73,345,381,101,333,74,329,341,102,377,82,339,103,375,327,83,340,104,376,328,81,105,337,373,325,78,106,338,374,326,79,107,336,372,324,80,677,673,680,672,247,272,319,122,195,320,248,120,196,270,318,271,246,121,197,275,322,250,125,194,273,323,251,123,192,274,321,249,124,193,128,267,245,317,201,268,243,315,126,202,269,244,316,127,203,241,266,313,131,200,242,264,314,129,198,240,265,312,130,199,669,684,681,676,145,307,172,403,367,173,146,404,368,308,171,306,144,402,366,310,168,148,406,370,311,169,149,407,371,309,170,147,405,369,401,305,151,178,365,303,152,179,399,363,304,150,177,400,364,154,301,174,397,361,155,302,175,398,362,153,300,176,396,360,683,666,675,679,117,295,283,23,259,284,118,21,260,296,282,294,119,22,258,298,286,116,19,262,299,287,114,20,263,297,285,115,18,261,14,293,108,281,257,291,109,279,12,255,292,110,280,13,256,111,289,277,17,253,112,290,278,15,254,113,288,276,16,252,661,663,662,671 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#a96a88e4cf05ff772a659e73be5ebad0179d3b86aa5fbe0be371d7ceb3ac096d, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 19:46:18 · history