Equation 677 Database

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Magma 994056cfa490…

magma 994056cfa490
Size
381
Isomorphism class hash
994056cfa4906fbb4e344c565b10ff01503c0f297e96067c4d127dcca3847e5d
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 23:23:05
Display reorder
380,171,166,175,150,155,160,146,135,140,131,120,125,202,207,197,187,192,182,50,46,47,48,49,243,100,291,96,116,106,111,39,272,212,11,40,12,77,280,72,85,90,82,257,249,254,278,262,267,45,297,44,42,43,41,222,227,217,237,287,232,324,323,325,326,327,328,361,365,351,340,332,347,357,376,337,370,174,169,179,154,159,164,149,139,144,134,124,129,201,206,196,185,190,181,13,14,15,16,17,240,104,294,99,119,109,114,22,271,210,24,25,23,79,284,74,89,94,80,255,245,251,275,261,265,32,295,31,29,30,28,221,226,215,236,286,231,302,300,301,304,305,303,364,369,354,344,331,346,355,379,335,374,172,167,177,152,157,162,147,137,142,132,122,127,203,208,198,188,193,183,21,19,20,18,10,241,102,292,97,117,107,112,51,273,213,2,52,3,76,281,71,86,91,81,258,248,253,277,263,268,57,298,56,54,55,53,223,228,218,238,288,233,313,312,314,315,316,317,362,366,352,341,333,348,358,375,338,372,170,165,176,151,156,161,145,136,141,130,121,126,200,205,195,186,191,180,36,37,38,34,35,242,101,290,95,115,105,110,26,270,211,0,27,1,78,282,73,87,92,84,256,247,252,276,260,266,5,296,4,7,6,33,220,225,216,235,285,230,309,311,310,308,306,307,360,367,350,342,330,345,356,377,336,371,173,168,178,153,158,163,148,138,143,133,123,128,204,209,199,189,194,184,9,8,69,67,68,244,103,293,98,118,108,113,60,274,214,61,59,58,75,283,70,88,93,83,259,246,250,279,264,269,65,299,64,62,63,66,224,229,219,239,289,234,322,321,320,329,319,318,363,368,353,343,334,349,359,378,339,373 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, 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 23:23:06 · history