Equation 677 Database

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Magma b7ec9579bd1f…

magma b7ec9579bd1f
Size
705
Isomorphism class hash
b7ec9579bd1fe0c6728667e2cacbf0056107b76c91cf9f774ef309eadd26f1df
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 18:24:11
Display reorder
660,1,391,331,552,492,0,550,389,329,490,2,551,390,330,491,3,387,327,548,488,4,388,328,549,489,5,386,326,547,487,382,322,6,543,483,380,320,7,541,481,381,321,8,542,482,325,385,9,546,486,323,383,10,544,484,324,384,11,545,485,684,680,673,674,141,214,207,293,427,139,294,212,208,425,140,295,213,206,426,137,217,210,292,423,138,215,211,290,424,136,216,209,291,422,220,205,132,284,418,218,203,130,285,416,219,204,131,286,417,201,223,135,287,421,202,221,133,288,419,200,222,134,289,420,670,663,661,666,153,298,579,480,86,151,478,296,577,84,152,479,297,578,85,149,301,575,476,89,150,299,576,477,87,148,300,574,475,88,304,570,144,471,92,302,568,142,469,90,303,569,143,470,91,573,307,147,474,95,571,305,145,472,93,572,306,146,473,94,678,687,682,686,55,655,652,654,657,56,638,639,636,641,54,646,647,644,649,58,623,621,622,625,59,631,629,630,633,57,615,613,614,617,186,127,53,168,555,187,125,51,169,553,185,126,52,170,554,604,606,49,608,609,128,183,50,167,556,129,184,48,166,557,703,699,698,704,124,250,238,337,504,122,335,248,236,502,123,336,249,237,503,120,253,241,333,500,121,251,239,334,501,119,252,240,332,499,256,244,115,343,495,254,242,113,341,493,255,243,114,342,494,247,259,118,339,498,245,257,116,340,496,246,258,117,338,497,689,691,694,693,98,154,528,591,456,96,589,155,526,454,97,590,156,527,455,101,157,524,587,452,99,158,525,588,453,100,159,523,586,451,160,519,104,582,447,161,517,102,580,445,162,518,103,581,446,522,163,107,585,450,520,164,105,583,448,521,165,106,584,449,672,664,669,667,267,72,355,516,37,268,514,73,353,38,266,515,74,354,36,270,75,351,512,40,271,76,352,513,41,269,77,350,511,39,78,346,265,507,43,79,344,263,505,44,80,345,264,506,42,349,81,261,510,46,347,82,262,508,47,348,83,260,509,45,692,695,696,690,22,315,540,468,603,23,466,316,538,601,21,467,314,539,602,18,318,536,464,599,19,319,537,465,600,20,317,535,463,598,313,531,13,459,594,311,529,14,457,592,312,530,12,458,593,534,309,16,462,597,532,310,17,460,595,533,308,15,461,596,677,688,685,683,276,656,658,653,659,277,637,640,642,643,275,645,648,650,651,272,624,626,620,627,273,632,634,628,635,274,616,618,612,619,432,560,282,111,565,430,558,283,109,563,431,559,281,110,564,611,610,278,605,607,561,429,279,112,566,562,428,280,108,567,702,701,697,700,172,196,233,379,365,173,377,194,234,366,171,378,195,235,367,175,199,232,375,364,176,197,230,376,362,174,198,231,374,363,191,224,178,370,356,192,225,179,368,357,193,226,177,369,358,227,190,181,373,359,228,188,182,371,360,229,189,180,372,361,662,665,668,671,30,444,60,415,398,31,413,442,61,399,32,414,443,62,400,33,440,63,411,401,34,441,64,412,402,35,439,65,410,403,435,66,28,406,396,433,67,29,404,397,434,68,27,405,395,69,438,24,409,392,70,436,25,407,393,71,437,26,408,394,675,681,676,679 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#82788998f5140702896c545961cafeebe136162a04e08140ecf7d45fe0422a3d, 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 18:24:12 · history