Equation 677 Database

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Magma 2218c69009d8…

magma 2218c69009d8
Size
381
Isomorphism class hash
2218c69009d89acaa19c5ee78e2db266d63e5b0aef1b80c80a187d6188412885
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 23:40:45
Display reorder
380,71,66,61,80,86,75,318,319,329,320,321,322,142,146,135,156,162,152,290,36,41,46,50,55,95,100,90,2,296,3,286,32,26,17,23,11,232,237,227,245,251,240,120,125,130,105,111,116,177,172,167,187,192,182,271,282,277,267,256,261,202,206,197,215,212,221,351,345,370,331,357,340,376,336,365,360,70,65,60,81,85,76,325,323,324,328,326,327,141,147,137,157,161,151,291,35,40,45,51,56,97,101,92,5,295,4,287,31,27,16,21,12,231,236,226,246,250,241,121,126,132,106,110,115,175,170,165,186,191,181,270,280,275,265,255,262,201,207,196,216,211,222,350,346,372,332,356,341,378,335,366,361,72,67,62,82,87,77,314,312,313,317,315,316,140,145,136,155,160,150,292,37,42,47,52,57,98,102,93,1,298,0,285,30,25,15,24,10,230,235,225,247,252,242,122,127,131,107,112,117,176,171,166,185,190,180,272,281,276,266,257,260,200,205,195,217,210,220,352,347,371,330,355,342,375,338,367,362,73,68,63,83,88,78,302,301,300,305,303,304,143,148,138,158,163,153,293,38,43,48,53,58,99,103,94,7,297,6,289,34,29,19,22,14,234,239,229,249,254,244,123,128,133,108,113,118,178,173,168,188,193,183,274,284,279,269,259,264,204,209,199,219,214,224,353,349,373,334,358,343,379,339,368,364,74,69,64,84,89,79,310,311,309,307,308,306,144,149,139,159,164,154,294,39,44,49,54,59,96,104,91,9,299,8,288,33,28,18,20,13,233,238,228,248,253,243,124,129,134,109,114,119,179,174,169,189,194,184,273,283,278,268,258,263,203,208,198,218,213,223,354,348,374,333,359,344,377,337,369,363 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#b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa, 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 23:40:46 · history