Equation 677 Database

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Magma 6761b60dd210…

magma 6761b60dd210
Size
381
Isomorphism class hash
6761b60dd210a26f63f621f836d81879608666f66361d26bee3062a3b27861d5
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 23:22:49
Display reorder
380,214,224,219,209,199,204,124,129,134,109,114,119,272,277,282,257,262,267,30,36,29,45,50,40,325,326,324,328,329,327,159,164,154,144,149,139,252,242,247,237,227,232,289,24,17,7,11,0,179,169,174,194,184,189,79,69,74,64,59,294,99,104,299,94,84,89,334,339,362,347,354,344,358,369,379,374,212,222,217,207,197,202,120,125,131,105,111,116,273,278,283,258,263,268,31,35,27,46,51,41,311,309,310,308,306,307,155,160,150,141,146,136,253,243,248,238,228,233,287,23,15,8,13,2,176,166,172,192,182,186,77,67,72,62,57,292,97,101,297,90,82,85,332,337,363,348,352,342,356,367,375,371,213,223,218,208,198,203,123,128,133,108,113,118,274,279,284,259,264,269,34,39,28,49,54,44,301,300,302,303,304,305,158,163,153,143,148,138,254,244,249,239,229,234,288,20,18,9,14,4,178,168,173,193,183,188,78,68,73,63,58,293,98,102,298,93,83,88,333,338,364,349,353,343,357,368,378,373,211,220,216,205,195,200,121,126,130,106,110,115,271,276,281,255,260,265,33,37,26,47,53,43,319,320,318,322,323,321,156,162,151,140,145,135,250,241,246,236,225,231,285,21,16,6,12,1,177,167,171,191,181,187,76,66,71,60,55,291,96,100,295,92,80,87,330,335,361,345,351,340,359,366,377,370,210,221,215,206,196,201,122,127,132,107,112,117,270,275,280,256,261,266,32,38,25,48,52,42,316,317,315,313,314,312,157,161,152,142,147,137,251,240,245,235,226,230,286,22,19,5,10,3,175,165,170,190,180,185,75,65,70,61,56,290,95,103,296,91,81,86,331,336,360,346,350,341,355,365,376,372 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, M = {68} 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 23:22:50 · history