Equation 677 Database

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Magma c8d1847e4667…

magma c8d1847e4667
Size
381
Isomorphism class hash
c8d1847e466743fbce4657d3c52c13a405032a33e49ec198d232a99b38265690
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 23:29:53
Display reorder
380,132,142,137,156,147,152,126,115,120,111,104,106,48,49,47,51,223,50,61,57,58,59,60,233,174,164,169,189,179,184,87,78,84,98,93,298,194,199,204,209,214,219,278,268,273,290,284,285,55,228,56,52,53,54,253,263,258,248,238,243,311,310,309,307,308,306,363,338,334,359,354,348,368,343,379,374,131,140,136,155,146,151,125,116,121,110,101,105,21,22,20,24,220,23,36,32,33,34,35,232,172,160,166,185,176,182,85,75,80,96,91,295,192,196,200,206,210,215,275,266,270,291,281,286,15,226,31,12,13,14,250,260,257,245,235,240,325,324,326,327,328,329,364,335,331,357,350,347,367,341,375,370,133,143,138,157,148,153,128,118,123,113,102,108,19,18,25,17,221,16,5,6,4,2,3,231,170,162,165,186,175,180,86,77,82,97,92,297,191,197,201,205,211,216,276,265,271,292,280,287,30,225,29,27,28,26,251,262,256,247,236,241,303,305,304,302,301,300,360,336,330,356,352,346,366,340,376,372,130,141,135,158,145,150,127,117,122,112,100,107,37,38,41,40,222,39,7,8,9,10,11,230,171,161,167,187,177,181,89,76,81,95,90,296,190,195,202,207,212,217,277,267,272,293,283,288,46,227,45,43,44,42,252,261,255,246,237,242,315,317,316,314,312,313,361,337,332,355,351,345,365,342,377,371,134,144,139,159,149,154,129,119,124,114,103,109,62,63,66,65,224,64,1,0,74,72,73,234,173,163,168,188,178,183,88,79,83,99,94,299,193,198,203,208,213,218,279,269,274,294,282,289,71,229,70,68,69,67,254,264,259,249,239,244,321,323,322,320,318,319,362,339,333,358,353,349,369,344,378,373 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, 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 23:29:54 · history