Equation 677 Database

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Magma 8ff0db35dc83…

magma 8ff0db35dc83
Size
381
Isomorphism class hash
8ff0db35dc83fb98316ff15a7fd6524f50d0f26b91817519b40cfc640bf181be
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 23:27:31
Display reorder
380,35,322,48,42,3,21,41,26,18,31,4,43,22,324,49,33,39,24,32,19,50,326,44,5,23,34,40,25,30,20,317,11,37,55,0,7,57,17,52,28,319,9,38,56,2,8,58,15,53,29,321,10,36,54,1,6,59,16,51,27,12,13,45,46,47,14,377,363,347,373,344,364,345,346,348,333,277,316,289,242,250,258,243,269,298,272,251,240,262,318,290,278,244,267,270,299,288,320,241,249,261,276,245,268,271,297,323,255,247,260,281,254,266,291,294,274,325,256,248,259,279,252,264,292,295,275,327,257,246,263,280,253,265,293,296,273,286,287,282,283,284,285,339,369,376,337,330,338,354,370,361,340,126,307,142,136,162,152,132,154,177,125,163,137,150,305,143,127,133,155,123,178,141,306,135,164,151,128,134,153,124,179,310,170,131,149,160,166,120,176,146,156,308,168,129,147,161,167,121,174,144,157,309,169,130,148,159,165,122,175,145,158,171,172,139,140,138,173,334,336,378,367,335,368,360,379,375,366,85,301,70,64,90,108,60,113,105,81,91,65,109,300,71,86,61,111,82,106,69,302,63,92,110,84,62,112,83,107,303,98,87,77,119,94,79,104,74,115,304,96,88,75,117,95,80,102,72,116,328,97,89,76,118,93,78,103,73,114,99,100,67,68,66,101,352,350,353,365,351,359,358,374,349,357,182,312,195,189,218,236,188,238,233,209,216,190,234,313,196,180,186,239,207,231,197,311,191,217,235,181,187,237,208,232,315,223,184,202,213,219,204,229,199,212,329,224,185,203,214,220,205,230,200,210,314,222,183,201,215,221,206,228,198,211,227,225,192,193,194,226,332,371,355,342,356,331,372,343,341,362 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#53fbdc66cf1e24939425582d82d07476a78d8f115434878d099d180ea3248471, 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 23:27:32 · history