Equation 677 Database

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Magma 4ef48f850a33…

magma 4ef48f850a33
Size
381
Isomorphism class hash
4ef48f850a33f6c28b33952b06539cfef3038106bcfbac6292f4e489ca7cabb6
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:36:46
Display reorder
380,263,258,252,273,268,26,31,36,40,286,46,278,127,117,121,111,101,107,50,55,60,66,291,71,162,167,172,177,182,187,295,95,91,82,87,75,192,197,202,207,212,217,302,301,300,305,303,304,152,156,146,136,142,132,248,238,243,233,223,228,282,7,2,19,20,12,337,357,368,332,346,363,350,341,376,370,262,256,250,271,266,27,32,37,42,287,47,275,125,115,120,110,102,105,52,57,62,67,292,72,160,165,170,176,181,186,297,97,92,80,85,77,191,196,201,205,210,215,315,316,317,312,313,314,150,155,145,135,140,131,247,237,242,230,221,226,281,6,0,15,21,10,336,355,365,330,347,361,352,344,377,372,260,255,253,272,267,28,33,38,43,288,48,277,128,118,123,113,103,108,53,58,63,68,293,73,163,168,173,178,183,188,298,98,93,83,88,78,193,198,203,208,213,218,324,325,326,327,328,329,153,158,148,138,143,133,246,235,240,231,222,227,283,8,3,17,23,13,338,358,366,333,348,362,353,342,378,373,264,259,254,274,269,29,34,39,44,289,49,279,129,119,124,114,104,109,54,59,64,69,294,74,164,169,174,179,184,189,299,99,94,84,89,79,194,199,204,209,214,219,307,308,306,310,311,309,154,159,149,139,144,134,249,239,244,234,224,229,284,9,4,18,24,14,339,359,369,334,349,364,354,343,379,374,261,257,251,270,265,25,30,35,41,285,45,276,126,116,122,112,100,106,51,56,61,65,290,70,161,166,171,175,180,185,296,96,90,81,86,76,190,195,200,206,211,216,320,318,319,323,321,322,151,157,147,137,141,130,245,236,241,232,220,225,280,5,1,16,22,11,335,356,367,331,345,360,351,340,375,371 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, M = {67} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:36:47 · history