Equation 677 Database

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Magma 5b1e18d881e9…

magma 5b1e18d881e9
Size
381
Isomorphism class hash
5b1e18d881e9693b6f0338f3156d07c0353ea398eb75c423c1a2853b903a9f14
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 23:49:26
Display reorder
380,30,25,35,41,270,46,193,198,203,178,183,188,233,223,228,218,208,213,51,56,275,66,70,61,16,22,11,9,266,2,250,256,261,236,241,246,100,105,110,115,286,120,88,76,83,96,91,280,155,296,150,165,170,161,316,315,317,312,313,314,132,126,137,141,146,290,336,370,360,345,356,331,366,350,340,378,34,28,39,44,274,49,191,196,200,176,180,185,232,222,227,217,207,212,53,58,278,68,73,63,18,23,13,5,267,3,253,257,262,237,243,248,103,108,113,118,288,123,87,78,82,98,93,283,158,298,153,168,173,163,319,318,320,321,322,323,131,128,136,143,148,293,337,372,363,348,358,332,368,353,343,375,32,29,38,43,273,48,194,199,204,179,184,189,234,224,229,219,209,214,54,59,279,69,74,64,19,24,14,8,269,4,254,258,264,239,244,249,104,109,114,119,289,124,89,79,84,99,94,284,159,299,154,169,174,164,305,304,303,300,302,301,133,129,138,144,149,294,339,374,364,349,359,334,369,354,344,379,33,27,37,42,272,47,192,197,202,177,182,187,230,221,225,215,206,210,52,57,277,67,72,62,17,21,12,7,265,1,252,255,260,235,242,247,102,107,112,117,287,122,85,77,80,97,92,282,157,297,152,167,172,162,309,311,310,308,306,307,134,127,139,142,147,292,335,371,362,347,357,330,367,352,342,377,31,26,36,40,271,45,190,195,201,175,181,186,231,220,226,216,205,211,50,55,276,65,71,60,15,20,10,6,268,0,251,259,263,238,240,245,101,106,111,116,285,121,86,75,81,95,90,281,156,295,151,166,171,160,328,327,329,324,325,326,130,125,135,140,145,291,338,373,361,346,355,333,365,351,341,376 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, M = {67} 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 23:49:27 · history