Equation 677 Database

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Magma 6b104ba9dfe8…

magma 6b104ba9dfe8
Size
705
Isomorphism class hash
6b104ba9dfe8152007b486a62e555a4754dd69fa85dfce5025dcde050bfb31d4
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 21:15:57
Display reorder
660,251,315,289,436,296,249,294,316,290,437,317,295,250,288,435,247,314,299,292,432,248,312,297,293,433,246,313,298,291,434,257,306,302,287,442,255,307,300,285,443,256,308,301,286,441,309,253,305,283,438,310,254,303,284,439,311,252,304,282,440,684,676,686,680,93,502,197,179,51,94,52,503,195,177,501,53,95,196,178,92,498,50,193,175,90,499,48,194,176,91,500,49,192,174,84,508,57,188,185,85,509,58,186,183,86,507,59,187,184,504,87,56,191,181,505,88,54,189,182,506,89,55,190,180,661,669,667,663,20,490,334,321,544,18,545,491,335,322,489,543,19,333,323,23,486,540,330,320,21,487,541,331,318,22,488,542,332,319,15,496,550,340,327,16,497,551,341,328,17,495,549,339,329,492,14,546,336,326,493,12,547,337,324,494,13,548,338,325,673,674,679,681,139,538,154,156,137,140,135,539,155,157,537,136,138,153,158,142,534,133,150,159,143,535,134,151,160,141,536,132,152,161,145,649,648,644,645,146,657,656,652,653,144,641,640,636,637,614,148,613,617,616,625,149,624,621,620,633,147,632,629,628,703,698,704,700,262,448,109,418,514,263,515,449,110,419,447,513,261,108,417,258,444,510,112,414,259,445,511,113,415,260,446,512,111,416,268,454,520,115,424,269,455,521,116,425,267,453,519,114,423,450,264,516,118,420,451,265,517,119,421,452,266,518,117,422,689,691,692,694,353,204,42,212,460,351,461,205,43,210,206,459,352,44,211,349,207,456,45,215,350,208,457,46,213,348,209,458,47,214,344,202,466,40,218,342,203,467,41,216,343,201,465,39,217,198,347,462,36,221,199,345,463,37,219,200,346,464,38,220,664,668,662,665,122,370,393,229,406,120,407,371,394,230,369,405,121,395,228,125,366,402,392,232,123,367,403,390,233,124,368,404,391,231,128,376,412,399,227,126,377,413,400,225,127,375,411,401,226,372,131,408,398,223,373,129,409,396,224,374,130,410,397,222,695,693,696,690,243,586,568,604,382,244,383,587,569,605,585,381,245,567,603,242,582,378,564,600,240,583,379,565,601,241,584,380,566,602,234,592,388,574,610,235,593,389,575,611,236,591,387,573,609,588,237,384,570,606,589,238,385,571,607,590,239,386,572,608,683,688,685,675,34,598,580,482,429,35,430,599,581,480,597,431,33,579,481,30,594,428,576,485,31,595,426,577,483,32,596,427,578,484,25,651,646,650,647,26,659,654,658,655,24,643,638,642,639,619,28,618,615,612,627,29,622,626,623,635,27,630,634,631,701,699,702,697,96,74,164,526,66,97,67,72,162,527,73,68,98,163,525,99,77,69,167,522,100,75,70,165,523,101,76,71,166,524,102,80,64,170,532,103,78,65,168,533,104,79,63,169,531,83,105,60,173,528,81,106,61,171,529,82,107,62,172,530,672,670,671,666,4,274,472,556,364,5,365,275,473,557,273,363,3,471,555,1,270,360,468,552,0,271,361,469,553,2,272,362,470,554,10,280,355,478,562,11,281,356,479,563,9,279,354,477,561,276,6,358,474,558,277,7,359,475,559,278,8,357,476,560,677,682,678,687 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#e1d7ea9e4f81623cd84c542145d634570787dd3fe7cd09a50189ca2a47386599, 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 21:15:58 · history