Equation 677 Database

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Magma 691969d00f86…

magma 691969d00f86
Size
381
Isomorphism class hash
691969d00f86c595e9247746a436b2e05ad2ca6352221b1e3f1db0340deb3628
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 23:29:37
Display reorder
380,10,9,11,12,291,17,235,242,247,252,257,262,159,164,169,174,179,184,19,20,18,230,51,33,93,91,92,228,94,95,218,99,100,101,97,98,302,301,300,305,303,304,278,268,273,299,280,289,89,90,88,96,223,87,194,189,199,204,209,214,136,131,128,145,151,141,348,364,369,338,351,374,334,343,358,376,14,16,15,52,290,13,236,241,246,250,255,261,157,162,167,172,177,182,32,31,34,231,50,8,28,26,27,225,29,30,217,86,85,83,84,82,315,316,317,312,313,314,276,265,271,296,281,286,24,25,23,22,221,21,193,188,197,202,207,212,137,130,125,146,150,140,345,362,366,337,352,372,332,341,356,375,79,78,77,81,293,80,238,243,248,253,258,263,155,160,165,171,176,181,73,74,72,233,76,75,68,67,71,227,69,70,216,4,5,63,6,7,329,327,328,326,324,325,277,267,272,297,283,287,2,66,3,65,222,64,192,186,196,201,205,210,139,132,127,147,152,143,347,361,367,336,353,371,331,342,357,378,39,38,37,36,292,35,237,240,245,251,256,260,156,161,166,170,175,180,47,45,46,232,48,49,42,40,41,226,43,44,215,61,62,60,58,59,322,323,321,319,320,318,275,266,270,295,282,285,54,55,53,57,220,56,191,187,195,200,206,211,135,133,126,148,153,142,346,360,365,335,350,370,330,340,355,377,109,108,107,111,294,110,239,244,249,254,259,264,158,163,168,173,178,183,103,104,102,234,106,105,122,120,121,229,123,124,219,112,113,114,0,1,307,308,306,310,311,309,279,269,274,298,284,288,118,119,117,116,224,115,190,185,198,203,208,213,138,134,129,149,154,144,349,363,368,339,354,373,333,344,359,379 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 = {68} 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 23:29:38 · history