Equation 677 Database

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Magma bd458731e4f9…

magma bd458731e4f9
Size
381
Isomorphism class hash
bd458731e4f92cb19e4aa967f4589b8d34152b6d97923f359652d18bc792f1d6
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 23:35:10
Display reorder
380,71,114,92,106,72,312,113,99,64,79,66,115,93,107,80,73,313,108,100,65,67,116,94,102,81,74,314,109,101,60,68,117,95,103,82,75,315,110,96,61,69,118,90,104,83,76,316,111,97,62,70,119,78,91,105,77,317,112,98,63,85,87,88,89,84,86,368,348,345,366,367,330,331,346,349,347,268,282,290,270,240,308,280,298,260,249,269,283,291,271,250,244,300,281,299,261,264,284,292,272,251,241,311,276,294,262,265,285,293,273,246,242,302,277,295,263,266,286,288,274,247,245,303,278,296,258,267,287,248,289,275,243,304,279,297,259,257,253,254,255,256,252,339,356,371,335,357,355,337,336,338,372,122,171,178,157,129,306,164,150,144,136,123,172,179,158,137,130,307,165,151,145,124,173,174,159,132,131,310,166,152,146,125,168,175,160,133,126,301,167,153,147,120,169,176,161,134,127,309,162,154,148,121,170,135,177,156,128,305,163,155,149,142,138,139,140,141,143,363,362,364,375,342,343,379,376,341,361,45,10,17,25,52,318,3,18,38,59,46,11,12,26,54,53,321,4,19,39,47,6,13,27,55,48,323,5,20,40,42,7,14,28,56,49,325,1,21,41,43,8,15,29,57,50,327,0,22,36,44,9,58,16,24,51,329,2,23,37,30,32,33,34,35,31,373,374,365,360,344,377,340,358,359,378,204,224,232,214,184,324,216,234,202,186,205,225,233,215,187,181,326,217,235,203,206,226,228,210,188,182,328,218,236,198,207,227,229,211,189,183,319,219,237,199,208,222,230,212,190,185,320,220,238,200,209,223,191,231,213,180,322,221,239,201,193,195,196,197,192,194,354,352,351,369,334,332,350,333,353,370 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#8b38eb0e4ba28ac2ddc3e949bb31ba8d1b7d25f5047510fd5f5ea112d69bd788, M = {66} 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 23:35:11 · history