Equation 677 Database

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Magma 07f6b09fab30…

magma 07f6b09fab30
Size
705
Isomorphism class hash
07f6b09fab30a4b401108741416a8256ab85fe676a5d39e5b45d1a59d533ce56
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 16:41:49
Display reorder
660,574,572,22,577,560,580,592,594,23,597,552,540,554,21,557,621,634,632,18,637,654,641,652,19,657,614,600,612,20,617,534,532,13,520,537,494,492,14,481,497,514,512,12,500,517,446,447,16,441,449,472,474,17,461,477,432,434,15,420,437,694,702,691,704,563,575,308,576,569,589,595,583,306,596,555,549,543,307,556,629,623,635,311,636,643,649,655,309,656,603,609,615,310,616,523,535,303,529,536,483,495,304,489,496,503,515,305,509,516,457,451,302,444,448,475,463,300,469,476,435,423,301,429,436,686,699,697,687,74,291,55,164,379,380,292,72,56,162,293,378,73,54,163,382,77,290,58,167,75,383,288,59,165,76,381,289,57,166,80,297,53,377,159,78,298,51,375,160,79,299,52,376,161,296,83,49,373,158,294,81,50,374,156,295,82,48,372,157,663,680,666,678,130,355,272,143,391,392,356,131,270,141,354,390,129,271,142,394,126,358,275,139,127,395,359,273,140,128,393,357,274,138,121,353,267,389,134,122,351,268,387,132,120,352,269,388,133,349,124,266,385,137,350,125,264,386,135,348,123,265,384,136,664,673,675,679,561,566,5,565,567,587,586,581,3,585,546,547,541,4,545,627,620,626,0,625,640,647,646,2,645,601,607,606,1,605,521,526,11,527,525,480,486,9,487,485,501,506,10,507,505,443,440,7,453,452,466,460,8,467,465,426,421,6,427,425,689,701,703,692,562,570,29,573,568,588,590,582,27,593,550,548,542,28,553,628,622,630,25,633,642,648,650,26,653,602,608,610,24,613,522,530,35,528,533,482,490,33,488,493,502,510,34,508,513,455,450,31,454,456,470,462,32,468,473,430,422,30,428,433,690,698,700,688,578,579,43,564,571,591,598,599,44,584,559,551,558,42,544,631,638,639,46,624,659,651,658,47,644,619,611,618,45,604,538,539,41,531,524,499,498,39,491,484,518,519,40,511,504,459,458,37,445,442,478,479,38,471,464,439,438,36,431,424,696,685,693,695,410,191,177,411,202,203,189,412,178,413,190,201,409,179,408,198,417,187,176,416,418,199,188,174,419,415,200,186,175,414,406,182,168,193,407,402,180,169,194,403,404,181,170,192,405,185,399,171,196,398,183,401,172,197,400,184,396,173,195,397,682,681,668,676,254,224,148,331,367,368,222,252,149,332,223,366,253,147,330,370,257,227,144,334,255,371,225,145,335,256,369,226,146,333,260,219,154,365,329,258,220,155,363,327,259,221,153,364,328,218,263,150,361,325,216,261,151,362,326,217,262,152,360,324,672,667,670,677,283,343,108,93,61,62,344,284,109,94,342,60,282,110,95,64,286,346,111,92,287,65,347,112,90,285,63,345,113,91,281,341,114,67,84,279,339,115,68,85,280,340,116,66,86,337,277,117,70,87,338,278,118,71,88,336,276,119,69,89,661,662,674,671,319,242,97,228,211,212,240,320,98,229,241,210,318,96,230,214,322,245,100,231,323,215,243,101,232,321,213,244,99,233,317,248,103,209,234,315,246,104,207,235,316,247,102,208,236,251,313,106,205,237,249,314,107,206,238,250,312,105,204,239,665,669,684,683 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#3a1e3dea02005faeb7a32ea89e0ebcd7060d0e295c5a20add7fb441719113d75, 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 16:41:51 · history