Equation 677 Database

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Magma 014110218b5f…

magma 014110218b5f
Size
381
Isomorphism class hash
014110218b5fa273eea8c3e4d3aafe9ec36800431b41cd67deaa972c8c063f3b
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 23:29:24
Display reorder
380,50,49,51,52,53,230,246,235,240,261,252,257,48,5,4,2,3,226,58,59,215,55,56,57,305,303,304,302,301,300,275,267,272,295,281,286,211,200,206,196,186,191,41,220,40,38,39,37,6,7,291,8,9,10,152,146,141,133,135,127,177,171,181,157,161,167,346,331,340,366,335,364,372,355,350,375,29,28,27,26,54,231,245,236,241,262,251,256,43,44,45,46,47,225,11,12,219,13,14,15,312,313,314,315,316,317,276,268,273,296,280,285,213,203,208,198,188,193,16,221,17,18,19,42,30,31,290,25,24,32,150,145,140,130,136,128,176,172,182,156,162,166,345,333,341,365,338,361,370,356,351,376,1,0,69,67,68,232,247,237,242,260,250,255,22,23,66,64,65,227,60,33,216,35,36,34,310,311,309,307,308,306,279,269,274,299,284,289,210,201,205,195,185,190,62,222,61,20,63,21,74,73,292,72,70,71,154,149,144,134,138,129,179,174,184,159,164,169,347,330,342,369,336,363,374,357,352,379,91,90,92,93,94,233,248,238,243,263,253,258,89,85,86,87,88,228,77,78,217,75,79,76,320,318,319,323,321,322,277,266,271,297,282,287,212,202,207,197,187,192,84,223,83,81,82,80,98,99,293,96,97,95,151,147,142,131,139,125,175,170,180,155,160,165,348,332,343,367,337,360,371,358,353,377,116,115,117,118,119,234,249,239,244,264,254,259,114,110,111,112,113,229,102,103,218,100,104,101,324,325,326,327,328,329,278,265,270,298,283,288,214,204,209,199,189,194,109,224,108,106,107,105,123,124,294,121,122,120,153,148,143,132,137,126,178,173,183,158,163,168,349,334,344,368,339,362,373,359,354,378 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, M = {66} 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 23:29:25 · history