Equation 677 Database

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Magma 3f13abb27946…

magma 3f13abb27946
Size
381
Isomorphism class hash
3f13abb27946fc90d71c853cc1c5d4b879a2799726e0b7648b3ab216a21612be
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 23:40:41
Display reorder
380,206,200,195,186,191,181,254,259,264,237,242,249,299,284,289,279,267,272,325,326,324,328,329,327,69,59,64,219,74,79,25,26,229,109,114,119,54,49,214,40,30,39,179,169,174,164,154,159,94,104,99,89,84,224,294,28,27,2,29,231,139,144,149,121,133,126,344,339,363,359,349,379,369,354,331,374,208,203,198,188,193,183,251,256,261,236,241,245,296,281,286,275,265,270,315,316,317,312,313,314,67,57,62,217,72,77,4,3,226,107,112,116,52,47,212,43,33,37,177,167,172,162,152,157,92,102,96,86,81,220,291,1,11,12,13,232,137,142,147,123,131,125,342,337,362,356,345,376,365,351,333,372,207,202,197,187,192,182,252,257,262,235,240,247,297,282,287,277,266,271,320,318,319,323,321,322,65,56,60,215,71,76,14,15,227,105,110,117,50,45,211,42,32,36,175,165,170,161,151,156,90,100,97,87,82,222,292,17,16,0,18,230,136,141,145,120,134,127,340,336,360,357,347,377,367,352,332,371,205,201,196,185,190,180,250,255,260,238,243,246,295,280,285,276,268,273,308,306,307,311,309,310,66,55,61,216,70,75,5,6,225,106,111,115,51,46,210,41,31,35,176,166,171,160,150,155,91,101,95,85,80,221,290,10,9,7,8,233,135,140,146,122,130,128,341,335,361,355,346,375,366,350,330,370,209,204,199,189,194,184,253,258,263,239,244,248,298,283,288,278,269,274,303,304,305,301,300,302,68,58,63,218,73,78,19,20,228,108,113,118,53,48,213,44,34,38,178,168,173,163,153,158,93,103,98,88,83,223,293,24,23,21,22,234,138,143,148,124,132,129,343,338,364,358,348,378,368,353,334,373 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 = {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 23:40:42 · history