Equation 677 Database

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Magma c61adc820f36…

magma c61adc820f36
Size
705
Isomorphism class hash
c61adc820f3682888971918e929658a82dcc1938f0658c6f25381fa4973f034e
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 16:47:40
Display reorder
704,561,560,562,563,1,559,5,6,4,0,2,3,179,158,159,180,157,178,161,175,162,176,160,177,156,185,154,186,155,184,152,181,153,182,151,183,139,171,140,169,141,170,142,174,143,172,144,173,145,166,146,167,147,168,148,165,149,163,150,164,677,676,687,686,544,546,545,542,543,541,537,535,536,540,538,539,430,408,406,431,407,432,404,429,405,427,403,428,414,436,412,437,413,438,410,435,411,433,409,434,396,420,394,418,395,419,392,416,393,417,391,415,402,426,400,424,401,425,398,422,399,423,397,421,664,665,671,670,558,557,556,553,554,555,548,549,547,551,552,550,590,591,593,592,589,588,596,597,598,599,595,594,602,603,604,605,601,600,608,609,610,611,607,606,570,571,573,572,575,574,569,568,565,564,567,566,582,583,584,585,586,587,580,581,576,577,578,579,674,675,682,683,31,33,32,36,34,35,39,37,38,42,40,41,456,478,479,454,480,455,477,452,475,453,476,451,484,462,485,460,486,461,483,458,481,459,482,457,468,444,466,442,467,443,464,440,465,441,463,439,474,450,472,448,473,449,470,446,471,447,469,445,696,697,702,703,49,51,50,54,52,53,46,47,48,45,43,44,224,200,201,225,199,223,203,227,204,228,202,226,206,230,207,231,205,229,209,233,210,234,208,232,188,212,189,213,187,211,191,215,192,216,190,214,194,218,195,219,193,217,197,221,198,222,196,220,688,689,693,692,64,66,65,62,63,61,57,55,56,60,58,59,636,637,639,638,641,640,643,642,644,645,646,647,649,648,651,650,653,652,654,655,657,656,659,658,614,615,616,617,612,613,621,620,622,623,619,618,626,627,628,629,625,624,632,633,634,635,631,630,662,663,669,668,82,84,83,80,81,79,90,88,89,86,87,85,327,295,296,325,297,326,298,330,299,328,300,329,301,322,302,323,303,324,304,321,305,319,306,320,286,307,287,308,288,309,285,310,283,311,284,312,292,313,293,314,294,315,291,316,289,317,290,318,691,690,695,694,12,11,10,7,8,9,17,18,16,13,14,15,134,107,108,135,106,133,103,137,104,138,105,136,113,132,114,130,112,131,109,128,110,129,111,127,99,119,97,120,98,118,102,115,100,116,101,117,94,125,95,126,96,124,93,121,91,122,92,123,673,672,684,685,341,340,342,339,337,338,331,332,333,334,335,336,374,347,348,375,346,373,343,377,344,378,345,376,353,372,354,370,352,371,349,368,350,369,351,367,386,359,387,360,385,358,389,355,390,356,388,357,384,365,382,366,383,364,380,361,381,362,379,363,699,698,700,701,29,28,30,27,25,26,19,20,21,22,23,24,512,492,490,513,491,511,488,515,489,516,487,514,498,518,496,519,497,517,494,521,495,522,493,520,524,502,525,503,523,504,527,501,528,499,526,500,530,508,531,509,529,510,533,507,534,505,532,506,661,660,666,667,76,78,77,74,75,73,69,67,68,72,70,71,271,247,248,272,249,273,250,274,251,275,252,276,253,277,254,278,255,279,256,280,257,281,258,282,236,260,237,261,235,259,239,263,240,264,238,262,242,266,243,267,241,265,245,269,246,270,244,268,679,678,681,680 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#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 16:47:41 · history