Equation 677 Database

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Magma 577e69e27f47…

magma 577e69e27f47
Size
705
Isomorphism class hash
577e69e27f47e6aeb8dbc62b4960fab116ba7f8607e4630cd12d4c99b1232109
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 18:11:43
Display reorder
660,301,77,289,313,277,302,278,75,290,314,76,276,300,288,312,297,73,273,285,309,298,74,274,286,310,299,72,275,287,311,68,283,295,307,319,284,66,296,308,320,306,282,67,294,318,71,279,291,303,315,69,280,292,304,316,70,281,293,305,317,685,686,688,687,444,119,429,410,426,445,427,117,430,408,118,428,446,431,409,443,115,425,432,406,441,116,423,433,407,442,114,424,434,405,125,417,435,450,416,418,123,436,451,414,452,419,124,437,415,121,420,438,449,412,122,421,439,447,413,120,422,440,448,411,701,702,704,703,65,271,619,591,606,63,607,272,617,592,270,605,64,618,590,61,267,602,615,594,62,268,603,616,595,60,269,604,614,593,262,597,610,56,589,598,263,608,54,587,55,596,261,609,588,265,600,613,59,585,266,601,611,57,586,264,599,612,58,584,670,669,672,671,160,457,148,172,136,161,137,458,149,173,456,135,159,147,171,156,453,132,144,168,157,454,133,145,169,158,455,134,146,170,463,127,139,151,163,128,464,140,152,164,150,126,462,138,162,459,130,142,154,166,460,131,143,155,167,461,129,141,153,165,680,677,679,678,481,181,476,494,510,482,511,182,474,492,180,512,480,475,493,477,184,509,472,490,478,185,507,473,491,479,183,508,471,489,179,501,467,487,500,502,177,465,488,498,486,503,178,466,499,175,504,470,483,496,176,505,468,484,497,174,506,469,485,495,689,690,691,692,202,566,234,215,231,203,232,564,235,213,565,233,201,236,214,198,562,230,237,211,199,563,228,238,212,200,561,229,239,210,572,222,240,208,221,223,570,241,209,219,207,224,571,242,220,568,225,243,204,217,569,226,244,205,218,567,227,245,206,216,697,698,700,699,24,30,655,627,642,25,643,31,653,628,32,641,26,654,626,27,33,638,651,630,28,34,639,652,631,29,35,640,650,629,36,633,646,22,625,634,37,644,23,623,21,632,38,645,624,39,636,649,18,621,40,637,647,19,622,41,635,648,20,620,661,662,664,663,343,86,331,356,362,344,360,84,332,354,85,361,342,330,355,339,89,358,327,352,340,87,359,328,353,341,88,357,329,351,81,368,322,334,347,366,82,323,335,345,333,367,83,321,346,80,364,325,337,350,78,365,326,338,348,79,363,324,336,349,682,681,684,683,249,97,580,9,13,250,14,98,578,10,96,12,251,579,8,248,100,16,583,5,246,101,17,581,6,247,99,15,582,7,95,257,576,255,1,11,93,577,256,0,656,657,94,658,659,91,260,575,254,3,92,258,573,252,4,90,259,574,253,2,693,694,696,695,526,195,514,538,551,527,549,196,515,539,197,550,525,513,537,529,194,554,517,541,530,192,552,518,542,528,193,553,516,540,186,557,520,532,544,555,187,521,533,545,531,556,188,519,543,189,560,523,535,547,190,558,524,536,548,191,559,522,534,546,666,665,668,667,398,111,381,46,375,396,376,112,382,47,113,377,397,383,45,394,110,378,384,42,395,108,379,385,43,393,109,380,386,44,102,373,387,404,52,374,103,388,402,53,403,372,104,389,51,105,369,390,400,48,106,370,391,401,49,107,371,392,399,50,674,673,676,675 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#69e303b0df9a949f679bcb1932ca3e0d44707fb71c41006ed01ea0a3f8179ab7, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 18:11:44 · history