Equation 677 Database

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Magma ffb74a21adc4…

magma ffb74a21adc4
Size
381
Isomorphism class hash
ffb74a21adc4243608c6d70dbba3729be60a93ec21d825d3d795754d9f2910e3
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 23:48:53
Display reorder
380,130,125,135,140,145,151,234,239,244,249,224,229,89,94,69,74,79,84,95,100,105,110,115,120,174,159,164,169,284,294,39,44,49,54,59,64,254,259,264,269,274,279,299,209,214,219,4,289,194,199,204,179,184,189,329,302,303,300,304,301,34,9,14,19,24,29,335,375,366,346,364,340,344,351,359,374,132,127,137,142,147,152,230,235,240,245,221,225,86,91,66,70,75,81,97,102,107,112,117,122,173,158,163,168,283,293,35,40,45,50,56,61,250,255,260,265,270,275,295,206,211,216,1,285,190,195,201,175,180,185,321,317,318,320,319,322,30,6,11,15,20,25,343,378,368,345,361,330,331,352,358,371,131,126,136,141,146,150,231,236,241,246,220,226,85,90,65,71,76,80,96,101,106,111,116,121,171,155,160,165,280,290,36,41,46,51,55,60,251,256,261,266,271,276,296,205,210,215,0,286,191,196,200,176,181,186,325,327,328,324,323,326,31,5,10,16,21,26,338,379,369,349,362,337,334,350,357,370,134,129,139,144,149,154,233,238,243,248,223,228,88,93,68,73,78,83,99,104,109,114,119,124,170,156,161,166,281,291,38,43,48,53,58,63,253,258,263,268,273,278,298,208,213,218,3,288,193,198,203,178,183,188,307,309,310,306,305,308,33,8,13,18,23,28,342,376,367,348,360,332,333,354,355,373,133,128,138,143,148,153,232,237,242,247,222,227,87,92,67,72,77,82,98,103,108,113,118,123,172,157,162,167,282,292,37,42,47,52,57,62,252,257,262,267,272,277,297,207,212,217,2,287,192,197,202,177,182,187,311,313,314,316,315,312,32,7,12,17,22,27,341,377,365,347,363,339,336,353,356,372 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#e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378, M = {71} 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 23:48:54 · history