Equation 677 Database

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Magma 8939b2772b0f…

magma 8939b2772b0f
Size
381
Isomorphism class hash
8939b2772b0f3c2d3f7786342fadba16ade4b27efdd3de36997e9044f441a054
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 23:40:55
Display reorder
380,230,180,280,45,71,135,223,273,173,68,128,33,155,205,255,15,51,111,192,242,292,9,82,105,87,147,7,247,297,197,313,314,312,316,317,315,165,216,265,26,61,121,98,133,38,228,278,178,104,93,8,202,252,152,261,211,160,55,115,20,75,140,44,237,187,287,372,340,353,336,377,367,348,330,356,360,232,182,282,47,72,137,220,270,171,66,126,31,157,207,257,17,52,112,190,241,291,6,81,103,86,145,1,246,296,196,301,300,302,303,304,305,167,217,267,27,62,122,96,131,35,226,276,175,101,91,2,201,251,151,262,212,162,57,117,22,76,142,40,236,186,285,371,342,351,337,375,366,345,332,357,361,231,181,281,46,70,136,221,271,170,65,125,30,156,206,256,16,50,110,191,240,290,3,80,100,85,146,0,245,295,195,308,306,307,311,309,310,166,215,266,25,60,120,95,130,36,225,275,176,102,92,5,200,250,150,260,210,161,56,116,21,77,141,41,235,185,286,370,341,350,335,376,365,346,331,355,363,233,183,283,48,73,138,222,272,172,67,127,32,158,208,258,18,53,113,193,243,293,12,83,107,88,148,11,248,298,198,323,321,322,320,318,319,168,218,268,28,63,123,97,132,37,227,277,177,106,94,10,203,253,153,263,213,163,58,118,23,78,143,42,238,188,288,373,343,352,338,378,369,347,333,358,362,234,184,284,49,74,139,224,274,174,69,129,34,159,209,259,19,54,114,194,244,294,14,84,109,89,149,13,249,299,199,324,325,326,327,328,329,169,219,269,29,64,124,99,134,39,229,279,179,108,90,4,204,254,154,264,214,164,59,119,24,79,144,43,239,189,289,374,344,354,339,379,368,349,334,359,364 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 = {74} 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 23:40:56 · history