Equation 677 Database

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Magma 298f24969aa2…

magma 298f24969aa2
Size
705
Isomorphism class hash
298f24969aa2df394bb9526890b8203ead9510bcdcee7a6bed48a1add421458a
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 16:47:24
Display reorder
704,334,333,335,332,330,331,324,325,326,327,328,329,341,366,367,339,368,340,369,337,370,338,371,336,364,347,365,345,363,346,360,343,361,344,362,342,317,378,315,379,316,380,313,381,314,382,312,383,323,376,321,377,322,375,319,372,320,373,318,374,693,692,703,702,561,560,559,558,563,562,553,554,552,556,557,555,161,184,185,159,183,160,180,157,181,158,182,156,190,167,191,165,189,166,186,163,187,164,188,162,173,196,171,197,172,195,169,192,170,193,168,194,179,202,177,203,178,201,175,198,176,199,174,200,688,689,696,697,61,60,62,63,64,65,66,67,68,69,70,71,216,246,247,217,248,218,249,219,250,220,251,221,244,222,245,223,243,224,240,225,241,226,242,227,228,207,229,208,230,209,231,206,232,204,233,205,234,213,235,214,236,215,237,212,238,210,239,211,669,668,677,676,9,11,10,7,8,6,2,1,0,5,3,4,608,609,611,610,607,606,601,600,603,602,605,604,590,591,592,593,588,589,596,597,598,599,594,595,569,568,565,564,567,566,575,574,570,571,572,573,581,580,576,577,579,578,587,586,582,583,585,584,662,663,682,683,255,257,256,253,254,252,263,261,262,259,260,258,538,95,93,539,94,537,91,534,92,535,90,536,86,529,84,530,85,528,89,532,87,533,88,531,74,107,72,105,73,106,77,103,75,104,76,102,80,98,78,96,79,97,83,101,81,99,82,100,686,687,699,698,436,435,437,434,432,433,441,442,443,440,438,439,481,460,461,482,459,480,456,484,457,485,458,483,466,487,467,488,465,486,462,490,463,491,464,489,493,471,494,472,492,473,496,470,497,468,495,469,499,477,500,478,498,479,502,476,503,474,501,475,690,691,701,700,14,13,12,16,17,15,19,20,18,22,23,21,515,30,31,513,32,514,33,511,34,512,35,510,28,506,29,504,27,505,24,509,25,507,26,508,527,546,525,547,526,548,523,549,524,550,522,551,518,544,516,545,517,543,521,540,519,541,520,542,685,684,695,694,58,57,59,56,54,55,48,49,50,51,52,53,125,148,149,123,147,124,144,121,145,122,146,120,154,131,155,129,153,130,150,127,151,128,152,126,137,113,135,111,136,112,133,109,134,110,132,108,143,119,141,117,142,118,139,115,140,116,138,114,665,664,678,679,453,455,454,451,452,450,446,444,445,449,447,448,392,412,413,390,411,391,408,395,409,393,410,394,418,387,419,388,417,389,414,386,415,384,416,385,404,424,402,425,403,423,407,420,405,421,406,422,399,430,400,431,401,429,398,426,396,427,397,428,666,667,680,681,350,349,348,352,353,351,355,356,354,358,359,357,637,636,638,639,640,641,643,642,645,644,647,646,648,649,650,651,653,652,654,655,656,657,659,658,631,630,632,633,634,635,628,629,624,625,626,627,613,612,615,614,617,616,618,619,621,620,623,622,661,660,673,672,36,38,37,41,39,40,44,42,43,47,45,46,309,277,278,310,276,311,280,308,281,306,279,307,283,300,284,301,282,302,286,303,287,304,285,305,265,290,266,288,264,289,268,293,269,291,267,292,271,296,272,294,270,295,274,299,275,297,273,298,670,671,675,674 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, M = {64} 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 16:47:28 · history