Equation 677 Database

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Magma 7e25a9ee262c…

magma 7e25a9ee262c
Size
381
Isomorphism class hash
7e25a9ee262c94b0809f290fad71bb7a667482884001804684172cbfdfb0ccc3
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 23:40:33
Display reorder
380,67,62,56,271,51,45,220,225,230,206,210,215,31,20,28,268,38,43,7,285,6,116,121,110,250,255,260,238,240,245,71,275,75,80,85,91,172,162,167,157,297,150,292,146,141,131,137,125,95,105,100,280,0,2,303,305,304,302,301,300,187,177,182,202,197,192,333,365,360,350,355,373,338,345,340,376,69,64,59,274,54,49,223,228,233,208,213,218,30,23,27,267,37,42,14,288,15,118,123,113,253,258,263,237,243,248,74,279,79,84,89,94,173,163,168,158,298,153,293,148,143,133,138,128,98,108,103,283,12,13,317,316,315,313,314,312,188,178,183,203,198,193,332,367,363,353,358,372,337,349,344,378,68,63,58,272,53,47,221,227,232,205,212,216,32,22,26,266,35,40,4,286,5,115,120,111,251,257,261,235,241,246,72,277,77,82,87,92,171,160,166,156,295,151,291,147,140,132,136,126,96,106,101,281,1,3,318,320,319,323,321,322,185,175,180,201,196,191,331,369,361,351,356,370,336,347,342,375,65,60,55,273,50,48,222,226,231,207,211,217,34,21,25,265,36,41,9,287,8,117,122,112,252,256,262,236,242,247,73,278,78,83,88,93,170,161,165,155,296,152,290,145,142,130,135,127,97,107,102,282,10,11,326,325,324,328,329,327,186,176,181,200,195,190,330,366,362,352,357,371,335,348,343,377,66,61,57,270,52,46,224,229,234,209,214,219,33,24,29,269,39,44,18,289,19,119,124,114,254,259,264,239,244,249,70,276,76,81,86,90,174,164,169,159,299,154,294,149,144,134,139,129,99,109,104,284,16,17,310,309,311,306,307,308,189,179,184,204,199,194,334,368,364,354,359,374,339,346,341,379 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 = {69} 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 23:40:34 · history