Equation 677 Database

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Magma 1d24f799fab4…

magma 1d24f799fab4
Size
396
Isomorphism class hash
1d24f799fab43c9248822d3817a504299c649458bc992143429a680f31019156
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 10:59:44
Display reorder
394,367,320,350,339,205,340,143,9,144,233,197,10,234,145,230,11,235,146,231,0,236,147,331,306,341,321,332,2,237,148,198,3,238,149,199,4,239,150,200,5,240,139,201,6,241,140,202,7,342,319,333,307,343,141,203,8,242,142,204,1,159,151,152,153,154,155,156,157,158,323,160,324,325,322,360,384,392,385,393,336,210,188,113,220,114,211,189,212,115,221,190,116,213,222,191,117,214,223,192,118,215,224,364,359,335,225,193,119,216,226,194,120,217,337,329,352,368,338,330,317,206,227,195,121,207,228,196,122,334,365,363,123,208,218,186,124,209,219,187,173,179,180,181,182,183,184,185,172,174,175,176,177,178,328,380,378,389,387,373,356,357,55,281,56,73,88,74,57,282,77,58,75,283,78,59,76,280,79,60,63,287,80,61,64,288,81,62,65,290,82,48,66,292,83,49,67,294,84,50,68,296,85,51,69,298,86,52,70,300,87,53,71,302,229,54,72,304,232,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,395,376,375,382,362,311,318,99,170,100,29,137,30,89,171,138,90,31,161,125,314,312,361,126,91,32,162,127,92,33,163,128,93,34,164,129,94,24,165,130,351,366,326,131,95,25,166,132,96,26,167,133,97,27,168,134,98,28,169,135,358,310,327,136,12,13,14,15,16,17,18,19,20,21,22,23,309,308,354,381,383,386,391,372,313,353,265,268,266,39,253,40,267,269,254,255,41,270,243,256,42,271,244,257,43,272,245,258,44,273,246,259,45,274,247,260,46,348,344,346,355,349,345,347,47,275,248,261,35,276,249,262,36,277,250,263,37,278,251,264,38,279,252,101,112,102,103,104,105,106,107,108,109,110,111,315,316,371,377,390,379,388 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#4e0a712b6cb26391345348f66522b2b04a60734e228aacf9c4259836b72d1a7d, 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 10:59:45 · history