Equation 677 Database

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Magma e07e831e23b2…

magma e07e831e23b2
Size
381
Isomorphism class hash
e07e831e23b2f5952232f74ea75723c17518e92de9c54d3232439fd698793150
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 23:49:51
Display reorder
380,235,230,225,246,251,241,42,46,36,291,32,27,116,106,111,132,121,127,196,201,205,211,216,220,2,7,12,16,288,23,305,303,304,302,301,300,167,172,177,181,185,190,55,50,295,71,61,66,282,272,277,267,256,261,155,150,161,137,142,147,76,87,82,100,91,96,332,355,360,379,345,351,337,370,341,368,239,234,229,249,254,244,44,49,39,294,34,29,117,107,112,130,120,125,199,204,209,214,219,224,4,9,14,18,289,24,312,313,314,315,316,317,165,170,176,184,189,194,57,52,297,72,62,67,284,274,279,269,259,264,159,154,164,136,140,146,75,85,80,104,92,97,334,359,364,378,349,354,339,374,344,369,236,232,227,245,250,240,41,47,37,292,31,26,115,105,110,131,122,126,195,200,206,210,215,221,0,5,10,15,286,20,325,326,324,328,329,327,166,171,175,180,186,191,56,51,296,70,60,65,281,271,276,265,255,260,156,151,160,135,141,145,77,86,81,101,90,95,330,356,361,375,346,350,336,371,340,366,238,233,228,248,253,243,43,48,38,293,33,28,119,109,114,134,124,129,198,203,208,213,218,223,1,6,11,17,285,21,320,318,319,323,321,322,169,174,179,183,188,193,59,54,299,74,64,69,283,273,278,268,258,263,158,153,163,139,144,149,79,89,84,103,94,99,333,358,363,377,348,353,338,373,343,367,237,231,226,247,252,242,40,45,35,290,30,25,118,108,113,133,123,128,197,202,207,212,217,222,3,8,13,19,287,22,311,309,310,308,306,307,168,173,178,182,187,192,58,53,298,73,63,68,280,270,275,266,257,262,157,152,162,138,143,148,78,88,83,102,93,98,331,357,362,376,347,352,335,372,342,365 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, M = {72} 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 23:49:52 · history