Equation 677 Database

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Magma 7e411a37924f…

magma 7e411a37924f
Size
381
Isomorphism class hash
7e411a37924f9c6f58103ea17f208ee71efc17a7f004d46c168fc02c2add0b1c
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 23:37:11
Display reorder
380,16,13,23,293,8,133,123,128,118,108,113,3,225,218,220,240,231,236,72,275,75,55,60,65,296,100,95,85,90,83,322,323,321,319,320,318,271,260,266,256,245,251,206,285,211,191,196,201,27,32,37,42,47,52,188,178,183,170,163,165,144,149,139,283,158,153,363,338,343,333,353,358,348,379,373,368,19,11,21,290,5,131,120,126,116,106,111,0,227,216,222,242,232,237,70,277,76,56,62,66,295,101,96,86,92,81,303,304,305,301,300,302,272,262,267,257,247,252,207,287,212,192,197,204,25,30,35,41,46,51,185,175,180,173,161,168,142,147,137,281,155,150,361,335,340,330,351,356,345,376,371,365,18,10,20,291,6,130,121,125,115,105,110,1,226,215,221,241,230,235,71,276,77,57,61,67,297,102,97,87,91,80,311,309,310,308,306,307,270,261,265,255,246,250,205,286,210,190,195,200,26,31,36,40,45,50,186,176,181,171,160,166,140,146,135,280,156,151,360,336,341,331,350,355,346,375,370,366,17,14,24,292,7,132,122,127,117,107,112,4,229,217,224,244,234,239,73,278,78,58,63,68,298,103,98,88,93,82,315,316,317,312,313,314,274,264,269,259,249,254,209,289,214,194,199,203,28,33,38,43,48,53,187,177,182,174,162,169,143,148,138,282,157,152,362,337,342,332,352,357,347,377,372,367,15,12,22,294,9,134,124,129,119,109,114,2,228,219,223,243,233,238,74,279,79,59,64,69,299,104,99,89,94,84,327,328,329,324,325,326,273,263,268,258,248,253,208,288,213,193,198,202,29,34,39,44,49,54,189,179,184,172,164,167,141,145,136,284,159,154,364,339,344,334,354,359,349,378,374,369 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, M = {73} 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 23:37:12 · history