Equation 677 Database

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Magma 849f5f31690d…

magma 849f5f31690d
Size
381
Isomorphism class hash
849f5f31690d631fd9512d6521529bb7047f991b0dfe123ffa1337285b4f4276
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 23:40:51
Display reorder
380,112,107,115,292,97,102,233,238,288,218,223,228,304,305,303,300,302,301,243,55,54,52,53,51,45,273,213,42,43,44,176,166,171,160,152,157,257,247,252,277,262,267,183,188,193,198,203,208,81,78,73,283,93,88,47,50,46,49,298,48,121,126,131,135,145,140,338,367,333,358,342,378,348,361,352,370,110,105,116,291,95,100,230,235,285,216,221,226,308,306,307,311,309,310,241,6,5,8,9,7,13,271,210,10,11,12,178,168,173,163,153,158,258,248,253,278,263,268,181,186,191,195,200,205,84,77,72,282,92,87,0,1,2,3,296,4,122,127,132,137,147,142,335,368,330,356,341,376,345,362,351,372,111,106,118,290,96,101,231,236,286,215,220,225,326,324,325,329,327,328,240,17,18,16,14,15,22,270,211,19,20,21,177,167,172,162,150,155,256,246,250,276,260,265,180,185,190,196,201,206,80,76,71,281,90,86,25,24,23,27,295,26,120,125,130,136,146,141,336,366,331,355,340,375,346,360,350,371,114,109,119,294,99,104,234,239,289,219,224,229,318,319,320,321,322,323,244,69,68,66,67,65,59,274,214,56,57,58,179,169,174,164,154,159,259,249,254,279,264,269,184,189,194,199,204,209,83,79,74,284,94,89,61,64,60,63,299,62,124,129,134,139,149,144,339,369,334,359,344,379,349,363,354,374,113,108,117,293,98,103,232,237,287,217,222,227,312,313,314,315,316,317,242,39,40,38,37,41,31,272,212,28,29,30,175,165,170,161,151,156,255,245,251,275,261,266,182,187,192,197,202,207,82,75,70,280,91,85,34,33,32,36,297,35,123,128,133,138,148,143,337,365,332,357,343,377,347,364,353,373 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#b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa, M = {73} 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 23:40:51 · history