Equation 677 Database

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Magma 1644014fcafc…

magma 1644014fcafc
Size
705
Isomorphism class hash
1644014fcafc6e6d873b95773cc2623e58667cbde771073fcc3724c3bdc91ccf
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 20:42:55
Display reorder
704,327,494,355,363,328,492,364,356,329,493,365,354,497,326,358,362,495,324,359,360,325,496,361,357,500,333,353,369,334,498,370,351,335,499,371,352,503,332,349,368,330,501,366,350,331,502,367,348,338,336,337,341,339,340,344,342,346,347,345,343,675,673,674,672,198,21,172,189,199,22,190,173,200,23,191,171,20,201,168,188,18,202,169,186,203,19,187,170,12,196,178,180,197,13,181,179,195,14,182,177,15,192,174,183,193,16,184,175,194,17,185,176,164,162,163,167,165,166,159,160,157,158,156,161,664,666,665,667,5,374,506,523,3,372,524,504,4,373,522,505,377,0,509,526,375,2,507,527,1,376,525,508,380,11,512,521,9,378,519,510,10,379,520,511,383,7,515,517,8,381,518,513,6,382,516,514,648,649,650,651,652,653,654,655,658,656,657,659,685,686,684,687,131,150,98,114,129,151,115,96,130,152,116,97,153,127,101,117,154,128,99,118,126,155,119,100,148,122,104,112,120,149,113,102,121,147,111,103,144,125,107,108,123,145,109,105,124,146,110,106,140,138,139,143,141,142,135,136,133,134,132,137,701,703,700,702,611,578,628,647,609,576,645,629,610,577,646,627,581,607,624,643,579,608,625,644,606,580,642,626,584,602,634,638,600,582,636,635,601,583,637,633,587,605,630,641,603,585,639,631,604,586,640,632,620,618,619,623,621,622,615,616,613,614,612,617,689,691,688,690,426,82,400,417,427,83,418,401,428,81,419,399,78,429,396,416,79,430,397,414,431,80,415,398,73,424,406,408,425,74,409,407,423,72,410,405,76,420,402,411,421,77,412,403,422,75,413,404,442,443,441,438,439,440,433,434,435,436,437,432,662,661,663,660,270,224,244,263,271,222,261,245,272,223,262,243,227,273,240,259,225,274,241,260,275,226,258,242,219,268,250,254,269,220,252,251,267,221,253,249,218,264,246,257,265,216,255,247,266,217,256,248,235,236,234,238,239,237,233,231,228,229,230,232,694,693,695,692,544,387,572,529,545,388,530,570,543,389,528,571,386,540,575,532,384,541,573,533,542,385,531,574,393,550,567,535,551,394,536,568,549,395,534,569,392,546,566,538,547,390,539,564,548,391,537,565,552,553,554,555,556,557,558,559,563,561,562,560,682,683,681,680,290,211,322,280,288,212,281,323,289,210,279,321,214,293,318,276,215,291,319,277,292,213,278,320,209,296,313,286,294,207,287,314,295,208,285,312,205,299,316,282,297,206,283,317,298,204,284,315,305,303,304,301,302,300,311,309,306,307,308,310,696,698,699,697,40,29,66,590,41,27,588,67,39,28,589,68,25,36,69,593,26,37,70,591,38,24,592,71,35,46,64,596,47,33,594,65,45,34,595,63,31,42,60,599,43,32,597,61,44,30,598,62,48,49,50,51,52,53,54,55,59,57,58,56,671,668,670,669,468,87,452,461,469,88,459,450,470,89,460,451,86,471,455,457,84,472,453,458,473,85,456,454,93,474,447,467,475,94,465,448,476,95,466,449,92,477,446,463,478,90,464,444,479,91,462,445,484,485,483,480,481,482,490,491,488,486,487,489,676,678,677,679 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#cce41c1fd55a940f76617a374756c8d0de5f99032cd8fe3feeb0eb2c48843df6, 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 20:42:56 · history