Equation 677 Database

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Magma 78685068950b…

magma 78685068950b
Size
381
Isomorphism class hash
78685068950b35b5569b439754b95933ad62c6a88d0a69698cbb91c2a891ec11
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 23:26:52
Display reorder
380,168,163,173,178,153,158,145,146,147,148,149,144,326,327,328,329,324,325,139,140,141,142,143,138,227,233,238,213,218,223,130,131,126,127,128,129,132,133,134,135,136,137,198,203,208,183,188,193,268,243,248,253,258,263,122,123,124,125,120,121,288,283,293,298,273,278,343,368,359,339,354,353,371,376,340,361,166,160,171,176,150,155,116,117,118,119,114,115,319,320,321,322,317,318,108,109,110,111,112,113,226,230,235,211,216,221,91,92,93,94,95,90,105,106,107,102,103,104,196,201,206,180,185,190,267,242,247,252,257,262,101,96,97,98,99,100,285,281,290,295,271,276,337,366,358,335,331,351,372,377,352,362,165,161,170,175,151,156,51,52,53,48,49,50,309,310,307,308,306,323,44,45,46,47,42,43,225,231,236,210,215,222,59,54,55,56,57,58,41,36,37,38,39,40,195,200,205,181,186,191,266,240,245,250,255,261,62,63,64,65,60,61,286,280,291,296,270,275,347,367,356,348,341,333,373,378,338,363,167,162,172,177,152,157,73,74,75,76,77,72,305,301,300,302,303,304,67,68,69,70,71,66,228,232,237,212,217,220,82,83,78,79,80,81,84,85,86,87,88,89,197,202,207,182,187,192,265,241,246,251,256,260,3,4,5,1,0,2,287,282,292,297,272,277,349,365,357,342,350,334,374,379,332,364,169,164,174,179,154,159,30,31,32,33,34,35,313,314,315,316,311,312,27,28,29,24,25,26,229,234,239,214,219,224,8,9,10,11,6,7,22,23,18,19,20,21,199,204,209,184,189,194,269,244,249,254,259,264,13,14,15,16,17,12,289,284,294,299,274,279,336,369,355,344,330,346,370,375,345,360 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {72} 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 23:26:53 · history