Equation 677 Database

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Magma afefcd835752…

magma afefcd835752
Size
396
Isomorphism class hash
afefcd835752eb7f59b3507346f960fea11beda93230811203ec174a78373477
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-05 11:11:04
Display reorder
380,358,320,313,310,132,321,266,23,267,54,269,24,270,55,276,25,274,56,199,26,125,46,314,311,326,318,315,27,126,47,34,16,127,48,28,17,128,49,29,18,129,50,30,19,130,51,31,20,327,319,312,309,328,52,32,21,131,53,33,22,63,65,66,57,58,59,60,61,62,322,64,323,324,325,355,386,383,385,389,351,204,240,268,271,205,241,275,277,206,230,133,213,207,231,134,214,208,232,135,215,209,233,359,364,342,234,136,216,210,235,137,217,211,345,329,343,363,346,306,344,200,236,3,218,201,237,1,219,341,366,354,212,202,238,2,263,203,239,265,182,174,175,176,177,178,179,180,181,183,184,185,186,173,338,375,381,377,393,373,357,356,79,281,102,93,80,282,103,94,81,283,104,95,67,280,105,82,68,287,106,83,69,288,107,84,70,290,108,85,71,292,109,86,72,294,96,87,73,296,97,88,74,298,98,89,75,300,99,90,76,302,100,91,77,304,101,92,78,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,379,394,395,378,361,353,334,124,142,273,154,110,143,279,155,111,144,254,156,112,330,349,362,113,145,255,157,114,146,256,158,115,147,257,159,116,148,258,160,117,331,368,332,118,138,259,150,119,139,260,151,120,140,261,152,121,141,262,153,122,360,350,333,123,253,245,246,247,248,249,250,251,252,242,243,244,347,348,367,382,387,390,391,372,352,337,40,188,272,172,0,187,278,161,149,198,220,162,41,189,221,163,42,190,222,164,43,191,223,165,44,192,224,166,45,193,225,335,316,339,365,336,317,340,226,167,35,194,227,168,36,195,228,169,37,196,229,170,38,197,264,171,39,4,15,5,6,7,8,9,10,11,12,13,14,307,308,371,392,376,388,384 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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, 5, B) with E = magma#98b16528073ac7b159dff157031893a3ff21fcc82cd65442bb1543925d4c715a, M = {75} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 79): MacNeish's product over GF(79); 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: 21.

last edited by qawbecrdtey at 2026-10-05 11:11:05 · history