Equation 677 Database

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Magma 53e5e251e9df…

magma 53e5e251e9df
Size
381
Isomorphism class hash
53e5e251e9df8a2db013c5cf837484a4735b5a8d686a01344a24eef8c657e871
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 23:29:45
Display reorder
380,174,184,179,169,159,164,242,247,237,257,262,252,14,231,45,11,12,13,74,227,73,10,8,9,215,54,55,53,51,52,316,317,315,313,314,312,277,267,272,299,281,289,189,194,199,204,209,214,145,151,141,130,135,125,221,19,20,21,22,40,47,46,48,49,50,292,335,351,369,334,347,357,341,373,364,377,171,181,176,165,155,160,240,245,235,256,260,251,72,232,71,69,70,68,7,226,6,4,5,67,218,104,105,103,101,102,310,311,309,307,308,306,275,265,270,296,282,286,187,192,197,202,208,211,148,152,142,133,137,126,220,39,38,36,37,35,26,25,27,28,29,291,338,350,365,331,346,355,340,371,361,376,172,182,177,167,157,162,241,246,236,255,261,250,75,230,41,44,42,43,66,225,65,63,64,62,216,56,15,18,16,17,305,303,304,302,301,300,276,266,271,295,280,285,185,190,195,201,206,212,146,150,140,131,136,128,222,60,59,57,58,61,31,30,32,33,34,290,336,352,366,332,345,356,342,372,362,375,173,183,178,168,158,163,244,249,239,259,264,254,118,234,117,1,119,0,115,229,114,2,116,3,219,109,110,108,106,107,323,321,322,320,318,319,279,269,274,298,284,288,188,193,198,203,207,213,149,154,144,134,138,129,224,112,111,23,113,24,120,122,121,124,123,294,339,354,368,333,349,359,344,374,363,379,170,180,175,166,156,161,243,248,238,258,263,253,94,233,95,91,92,93,90,228,89,87,88,86,217,80,79,77,78,76,326,324,325,329,327,328,278,268,273,297,283,287,186,191,196,200,205,210,147,153,143,132,139,127,223,84,83,81,82,85,97,96,98,99,100,293,337,353,367,330,348,358,343,370,360,378 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 = {70} 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 23:29:46 · history