Equation 677 Database

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Magma a7cc19250ce3…

magma a7cc19250ce3
Size
705
Isomorphism class hash
a7cc19250ce30f53d0d33646b3cba46a661347509ae806824f555c75cbbccdb5
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 17:43:42
Display reorder
704,215,189,342,201,213,190,343,202,214,191,344,203,211,188,345,200,212,186,346,198,210,187,347,199,340,206,180,192,341,204,181,193,339,205,182,194,209,336,183,195,207,337,184,196,208,338,185,197,218,216,217,221,219,220,224,222,226,227,225,223,675,674,673,672,576,562,7,568,577,563,8,569,578,561,6,567,579,558,10,564,580,559,11,565,581,560,9,566,5,582,553,574,3,583,554,575,4,584,552,573,585,0,556,570,586,2,557,571,587,1,555,572,592,593,591,588,589,590,598,599,596,594,595,597,667,666,664,665,380,356,41,368,378,354,39,366,379,355,40,367,383,359,37,371,381,357,38,369,382,358,36,370,47,375,351,363,45,376,352,364,46,377,353,365,374,43,350,362,372,44,348,360,373,42,349,361,648,649,650,651,652,653,654,655,658,656,657,659,685,686,684,687,77,49,104,60,75,50,102,61,76,48,103,62,73,52,107,63,74,53,105,64,72,51,106,65,99,83,55,66,100,81,56,67,101,82,54,68,79,98,58,69,80,96,59,70,78,97,57,71,90,91,92,93,94,95,88,89,86,84,85,87,701,700,703,702,465,489,110,453,466,490,108,454,467,491,109,455,464,488,113,452,462,486,111,450,463,487,112,451,116,456,480,444,114,457,481,445,115,458,482,446,459,119,483,447,460,117,484,448,461,118,485,449,478,479,477,474,475,476,469,470,471,472,473,468,690,691,689,688,249,273,440,287,250,274,438,285,251,275,439,286,248,272,443,283,246,270,441,284,247,271,442,282,435,240,264,278,436,241,265,276,437,242,266,277,243,434,267,281,244,432,268,279,245,433,269,280,262,263,261,258,259,260,253,254,255,256,257,252,660,661,662,663,163,135,494,149,164,136,492,147,162,137,493,148,166,134,497,145,167,132,495,146,165,133,496,144,500,161,141,155,498,159,142,153,499,160,143,154,157,503,140,151,158,501,138,152,156,502,139,150,124,125,123,120,121,122,130,131,128,126,127,129,694,695,693,692,424,399,239,411,425,400,237,412,423,401,238,413,420,398,235,410,421,396,236,408,422,397,234,409,230,430,405,417,228,431,406,418,229,429,407,419,426,233,404,416,427,231,402,414,428,232,403,415,388,389,387,384,385,386,394,395,392,390,391,393,680,683,682,681,518,544,173,508,516,545,171,509,517,543,172,507,521,540,169,504,519,541,170,505,520,542,168,506,179,524,550,514,177,522,551,515,178,523,549,513,527,175,546,510,525,176,547,511,526,174,548,512,539,537,538,535,536,534,530,528,532,533,531,529,697,699,698,696,612,642,35,604,613,643,33,605,614,644,34,603,615,645,31,600,616,646,32,601,617,647,30,602,26,618,640,610,24,619,641,611,25,620,639,609,621,29,636,606,622,27,637,607,623,28,638,608,627,628,629,626,624,625,633,634,631,632,630,635,671,670,668,669,316,290,22,310,317,288,23,311,315,289,21,309,312,293,18,306,313,291,19,307,314,292,20,308,13,322,296,301,14,323,294,302,12,321,295,300,318,16,299,304,319,17,297,305,320,15,298,303,325,326,324,328,329,327,331,332,333,334,335,330,676,677,678,679 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#616ee92b4c2e3f87630606dae5e5d5a5d531c0e51b30b7b61db0c949f5d47644, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 17:43:43 · history