Equation 677 Database

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Magma d4f08ea2a527…

magma d4f08ea2a527
Size
381
Isomorphism class hash
d4f08ea2a52719d78c28bc0825896b6a82005e4ae42c77dcacb3d89f69630720
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 23:20:56
Display reorder
380,122,272,151,183,213,242,266,296,146,173,208,238,150,182,212,241,271,120,306,307,308,309,310,311,54,55,56,57,58,59,267,299,149,179,209,239,291,141,166,202,232,261,142,167,203,233,262,292,41,36,37,38,39,40,47,42,43,44,45,46,48,49,50,51,52,53,366,338,355,379,359,332,378,331,365,335,139,289,164,200,230,259,269,298,148,178,181,210,165,201,231,260,290,140,316,317,312,313,314,315,86,87,88,89,85,84,240,270,121,174,180,211,294,144,168,206,236,264,145,169,207,237,265,295,118,119,115,114,116,117,112,113,110,111,108,109,93,95,90,91,94,92,361,330,358,371,336,357,377,337,369,354,124,274,153,185,215,244,263,293,143,172,204,234,152,184,214,243,273,123,319,320,321,322,323,318,35,30,31,32,33,34,268,297,147,177,205,235,281,131,158,192,222,251,132,159,193,223,252,282,81,82,83,78,79,80,73,74,75,76,77,72,29,24,25,26,27,28,364,340,347,370,356,334,375,333,360,339,130,280,157,191,221,250,247,277,127,175,188,218,156,190,220,249,279,129,324,325,326,327,328,329,3,4,5,1,0,2,248,278,128,176,189,219,285,135,162,196,226,255,136,163,197,227,256,286,15,16,17,12,13,14,21,22,23,18,19,20,11,6,7,8,9,10,367,346,351,374,344,350,373,343,368,345,134,284,161,195,225,254,257,287,137,171,198,228,160,194,224,253,283,133,303,304,305,301,300,302,106,107,102,103,104,105,258,288,138,170,199,229,276,126,155,187,217,246,125,154,186,216,245,275,63,64,65,60,61,62,69,70,71,66,67,68,100,101,96,97,98,99,363,349,341,372,353,342,376,352,362,348 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {71} 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 23:20:57 · history